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(EUUQUU IUTUU (夡j.[" endstream endobj 172 0 obj <> endobj 173 0 obj <> endobj 174 0 obj <> endobj 175 0 obj <> endobj 163 0 obj <>stream q 403.1999969 0 0 336.9600067 0 239.0399933 cm /Im0 Do Q q 403.1999969 0 0 239.0399933 0 0 cm /Im1 Do Q BT /T1_0 1 Tf 0.05 Tc 3 Tr 9.416 0 0 8.1 36.32 507.4299 Tm (Proof: )Tj 0.0484 Tc 8.1 0 0 8.1 67.44 507.4299 Tm (In )Tj 0.05 Tc 9.0161 0 0 8.1 78.28 507.4299 Tm (the )Tj 0.0313 Tc 8.1 0 0 8.1 36.71 424.63 Tm (replace: )Tj /T1_1 1 Tf 0.05 Tc 9.8334 0 0 8 49.95 286.21 Tm (It )Tj /T1_0 1 Tf 8.2195 0 0 8.1 67.95 286.21 Tm (easy )Tj 9.7782 0 0 8 36.65 250.9299 Tm (I,emma )Tj 8.7898 0 0 8 72.13 250.9299 Tm (2.7 )Tj /T1_2 1 Tf 9.1462 0 0 7.9001 37 240.31 Tm (of )Tj -0.0102 Tc 8.8 0 0 8.8 46.97 240.31 Tm (St )Tj 0.05 Tc 8.3807 0 0 7.9001 57.99 240.31 Tm (satisfying )Tj /T1_0 1 Tf 9.3502 0 0 8.1 36.5 214.9299 Tm (Proof: )Tj 8.1256 0 0 8.1 67.46 214.9299 Tm (Let )Tj -0.035 Tc 7.7097 0 0 8.1 83.06 214.9299 Tm (?rl )Tj 0.05 Tc 8.4566 0 0 8.1 36.8 204.49 Tm (\(a\)\), )Tj 8.5774 0 0 8.1 55.89 204.49 Tm (and )Tj 8.3199 0 0 8.1 72.29 204.49 Tm (let )Tj /C0_0 1 Tf 0 Tc 5.0401 0 0 52.5601 133.39 445.33 Tm <005B007E0020>Tj /T1_0 1 Tf 0.05 Tc 8.7642 0 0 8.1 195.76 507.4299 Tm (of )Tj 0 Tc 7.7 0 0 7.7 152.56 491.77 Tm [(0 )-933(0 )]TJ 8 0 0 8 178.64 491.95 Tm (1 )Tj /T1_1 1 Tf 7.8001 0 0 7.8001 152.75 481.33 Tm [(1 )-851(1 )]TJ /T1_0 1 Tf 8.1 0 0 8.1 178.48 481.33 Tm (0 )Tj 8 0 0 8 166.04 471.0699 Tm (1 )Tj /T1_1 1 Tf 1.623 -0.022 Td (1 )Tj /T1_0 1 Tf 7.7 0 0 7.7 191.44 470.89 Tm (0 )Tj -5.026 -1.379 Td (0 )Tj /T1_1 1 Tf 7.8001 0 0 7.8001 166.07 460.45 Tm (1 )Tj /T1_0 1 Tf 7.7 0 0 7.7 152.74 449.83 Tm (0 )Tj 8.4 0 0 8.4 165.87 449.83 Tm (0 )Tj 7.5001 0 0 7.5001 165.88 439.39 Tm (0 )Tj 7.7 0 0 7.7 178.66 439.39 Tm [(0 )-910(0 )]TJ 0.05 Tc 8.4307 0 0 8.1 155.87 268.21 Tm (with )Tj /T1_2 1 Tf 0 Tc 8.4 0 0 8.4 175.84 268.21 Tm (k )Tj /T1_0 1 Tf -0.035 Tc 5.4466 0 0 8.4 183.28 268.21 Tm (::.: )Tj 0.0209 Tc 8.1 0 0 8.1 191.67 268.21 Tm (4. )Tj 0 Tc 7.7 0 0 7.7 204.22 491.95 Tm [(0 )-863(0 )]TJ 0 -1.356 TD (0 )Tj 1.613 -0.023 Td (0 )Tj /T1_1 1 Tf 7.8001 0 0 7.8001 229.79 481.5099 Tm (1 )Tj 8 0 0 8 204.94 471.0699 Tm (1 )Tj /T1_0 1 Tf 7.7 0 0 7.7 217 471.0699 Tm (0 )Tj /T1_1 1 Tf 8.1 0 0 8.1 229.58 470.89 Tm (0 )Tj /T1_0 1 Tf 7.7 0 0 7.7 204.58 460.45 Tm (0 )Tj 8 0 0 8 217.16 460.63 Tm (1 )Tj 7.7 0 0 7.7 229.6 460.45 Tm (0 )Tj /T1_1 1 Tf 7.8001 0 0 7.8001 217.19 450.19 Tm (1 )Tj /T1_2 1 Tf 0.05 Tc 8.3601 0 0 7.9001 228.19 250.9299 Tm (at )Tj /T1_0 1 Tf 8.4691 0 0 8.1 49.97 194.41 Tm (The )Tj 8.5533 0 0 8.1 67.69 194.41 Tm (proof )Tj 8.9729 0 0 8.1 90.63 194.41 Tm (of )Tj /C0_0 1 Tf 0 Tc 4.5601 0 0 5.9401 101.53 194.41 Tm <005D007E0065006D006D00610020>Tj /T1_0 1 Tf 0.05 Tc 8.1117 0 0 8.1 199.97 194.41 Tm (remains )Tj -0.005 Tc 8.1 0 0 8.1 36.53 183.97 Tm (we )Tj 0.0467 Tc 1.556 0 Td (have )Tj 0.05 Tc 9.3029 0 0 8.1 68.92 183.97 Tm (that )Tj -0.035 Tc 6.4055 0 0 8.1 101.44 183.97 Tm (?r2 )Tj 0.05 Tc 8.5774 0 0 8.1 112.77 183.97 Tm (and )Tj -0.035 Tc 6.211 0 0 8.1 129.7 183.97 Tm (?r} )Tj 0 Tc 8.1 0 0 8.1 140.67 183.97 Tm (-)Tj -0.035 Tc 6.558 0 0 8.1 148.96 183.97 Tm (?r2 )Tj 0.05 Tc 8.5325 0 0 8.1 160.65 183.97 Tm (are )Tj 8.4732 0 0 8.1 175.15 183.97 Tm (permutations )Tj 8.3469 0 0 8.1 227.26 183.97 Tm (of )Tj 0.0029 Tc 8.1 0 0 8.1 36.61 150.31 Tm (so )Tj 0.018 Tc 1.315 0 Td (clearlY?r3 )Tj 0 Tc 5.956 0 Td (a )Tj 0.05 Tc 8.5973 0 0 8.1 103.33 150.31 Tm (permutation )Tj 8.5556 0 0 8.1 152.38 150.31 Tm (of )Tj /T1_2 1 Tf 0.0233 Tc 8.8 0 0 8.8 162.71 150.31 Tm (St. )Tj /T1_0 1 Tf 0.0245 Tc 8.1 0 0 8.1 176.93 150.31 Tm (Also )Tj 0 Tc 8.3 0 0 8.3 123.86 127.2599 Tm ({ )Tj 0.05 Tc 10.7758 0 0 8.3 131.45 135.19 Tm (-2i )Tj /T1_3 1 Tf 0 Tc 7.3001 0 0 7.3001 130.92 124.03 Tm (t )Tj /T1_1 1 Tf 12.5 0 0 12.5 136.06 124.03 Tm (+ )Tj /T1_0 1 Tf 0.05 Tc 8.4268 0 0 8.1 144.51 124.03 Tm (4i )Tj /T1_3 1 Tf 12.8446 0 0 8.4 160.78 135.0099 Tm (\(i=l, )Tj 9.7744 0 0 8.4 187.04 135.0099 Tm (... )Tj /T1_2 1 Tf 10.2405 0 0 9.1 198.76 135.0099 Tm (,t )Tj /T1_3 1 Tf -0.035 Tc 8.0108 0 0 8.4 215.47 135.0099 Tm (1\) )Tj /T1_2 1 Tf 0.05 Tc 12.1211 0 0 9.1 160.86 124.5699 Tm (\(i=t+l, )Tj 10.5133 0 0 9.1 200.96 124.5699 Tm (... )Tj 0 Tc 9.1 0 0 9.1 212.25 124.5699 Tm (, )Tj 0.05 Tc 11.8269 0 0 9.1 225.09 124.5699 Tm (-1\) )Tj /T1_0 1 Tf -0.0193 Tc 8.1 0 0 8.1 36.79 109.45 Tm (so )Tj -0.035 Tc 7.3336 0 0 8.1 47.25 109.45 Tm (?rl )Tj 0 Tc 8.1 0 0 8.1 57.87 109.45 Tm (-)Tj -0.035 Tc 6.4055 0 0 8.1 66.16 109.45 Tm (?r3 )Tj 0.0168 Tc 8.1 0 0 8.1 77.51 109.45 Tm (is )Tj 0.05 Tc 8.7327 0 0 8.1 94.15 109.45 Tm (permutation )Tj 8.5556 0 0 8.1 143.92 109.45 Tm (of )Tj /T1_2 1 Tf 0.0233 Tc 8.8 0 0 8.8 154.43 109.45 Tm (St. )Tj /T1_0 1 Tf 0.05 Tc 8.1533 0 0 8.1 168.63 109.45 Tm (Finally )Tj /T1_1 1 Tf 0 Tc 8 0 0 8 225.22 92.35 Tm [(\( )207(i )]TJ /T1_0 1 Tf 0.0029 Tc 8.1 0 0 8.1 36.61 75.78 Tm (so )Tj -0.035 Tc 6.253 0 0 8.1 47.26 75.78 Tm (?r2 )Tj 0 Tc 8.1 0 0 8.1 57.87 75.78 Tm (-)Tj -0.035 Tc 6.253 0 0 8.1 66.34 75.78 Tm (?r3 )Tj 0.0168 Tc 8.1 0 0 8.1 77.51 75.78 Tm (is )Tj 0 Tc 1.154 0 Td (a )Tj 0.05 Tc 8.7327 0 0 8.1 94.33 75.78 Tm (permutation )Tj 8.3469 0 0 8.1 144.1 75.78 Tm (of )Tj /T1_2 1 Tf 0.0233 Tc 8.8 0 0 8.8 154.43 75.78 Tm (St. )Tj /T1_0 1 Tf -0.0185 Tc 8.9 0 0 8.9 196.43 46.09 Tm (12 )Tj 0 Tc 7.7 0 0 7.7 242.2 481.33 Tm (0 )Tj 0.023 -2.712 Td (0 )Tj 8.1 0 0 8.1 242.38 439.5699 Tm (0 )Tj 0.0429 Tc 8.2 0 0 8.2 302.12 532.45 Tm (6. )Tj -0.035 Tc 19.9105 0 0 28.8 254.91 449.47 Tm (:\) )Tj /T1_3 1 Tf 0.05 Tc 8.2097 0 0 7.3001 273.83 286.03 Tm (3,2t; )Tj /T1_2 1 Tf 8.5244 0 0 8.2 277.67 250.9299 Tm (permutations )Tj /T1_0 1 Tf -0.0035 Tc 8.1 0 0 8.1 330.2 250.9299 Tm (?rl, )Tj -0.035 Tc 7.2246 0 0 8.1 342.81 250.9299 Tm (?r2, )Tj 0.05 Tc 8.9729 0 0 8.1 270.27 215.11 Tm (of )Tj 8.6171 0 0 8.1 280.39 215.11 Tm (Lemma )Tj 0.0296 Tc 8.1 0 0 8.1 252.45 194.05 Tm (for )Tj 0.0292 Tc 1.69 0 Td (all )Tj /T1_3 1 Tf 0 Tc 7.3001 0 0 7.3001 278.34 194.05 Tm (t )Tj /T1_1 1 Tf -0.035 Tc 5.0848 0 0 9.9 284.32 194.05 Tm (== )Tj /T1_0 1 Tf 0 Tc 8.2 0 0 8.2 294.02 194.05 Tm (1 )Tj 0.05 Tc 8.9729 0 0 8.1 300.87 194.05 Tm (or )Tj 0 Tc 8.2 0 0 8.2 312.01 194.05 Tm (5 )Tj 0.0391 Tc 8.1 0 0 8.1 251.5 183.97 Tm (Now )Tj /T1_2 1 Tf 0.05 Tc 11.674 0 0 10.9 264.44 128.89 Tm (=t+ )Tj /T1_3 1 Tf 0 Tc 11.7 0 0 11.7 304.61 129.0699 Tm (+ )Tj /T1_2 1 Tf 0.0361 Tc 9 0 0 9 313.45 129.0699 Tm (t\) )Tj /T1_0 1 Tf 0.0251 Tc 8.1 0 0 8.1 355.93 194.05 Tm (so )Tj /T1_1 1 Tf 0 Tc 8.7 0 0 8.7 357.76 75.96 Tm (o )Tj ET endstream endobj 169 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 53193/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream +[3DGӲB;՝F#Jl#!;5I]$!C'i "mGM0>N A:5+#Y DtOGd|DuGDu#B";"9&ˑO4ax";#uFhDt]2:"h(GTGQqQNT(xAw ;B":l@ @ 2?A%ˤN SA4& GTY! 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0 7.9001 163.24 464.95 Tm (... )Tj 0 Tc 7.9001 0 0 7.9001 173.76 464.95 Tm (, )Tj /T1_1 1 Tf 0.0256 Tc 7.4001 0 0 7.4001 177.35 464.95 Tm (16u )Tj /T1_0 1 Tf 0 Tc 7.9001 0 0 7.9001 190.94 464.95 Tm (+ )Tj -0.0307 Tc 0.996 0 Td (3} )Tj /T1_1 1 Tf 0.05 Tc 9.0581 0 0 7.4001 93.67 455.41 Tm (i=16u+5,16u+7, )Tj 9.8422 0 0 7.4001 163.35 455.41 Tm (... )Tj 8.681 0 0 7.4001 173.91 455.41 Tm (,18u+ )Tj /T1_0 1 Tf 0.0149 Tc 8.2 0 0 8.2 199.56 455.41 Tm (I} )Tj /T1_1 1 Tf 0.05 Tc 7.7768 0 0 7.4001 93.68 446.41 Tm (i::::16u+6,16u )Tj 0.0188 Tc 7.4001 0 0 7.4001 155.62 446.41 Tm (8, )Tj 0.05 Tc 9.8422 0 0 7.4001 163.35 446.41 Tm (... )Tj 8.9226 0 0 7.4001 174.09 446.41 Tm (,18u+2} )Tj /T1_3 1 Tf 0 Tc 7.3001 0 0 7.3001 93.9 436.87 Tm (i )Tj /T1_1 1 Tf 0.05 Tc 9.162 0 0 7.4001 118.19 436.87 Tm (+3,18u+4} )Tj 0 Tc 7.7 0 0 7.7 93.87 427.87 Tm (i )Tj 0.05 Tc 7.6591 0 0 7.4001 98.42 427.87 Tm (=18u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 118.27 427.87 Tm (+ )Tj /T1_0 1 Tf -0.0323 Tc 7.9001 0 0 7.9001 126.25 427.87 Tm (5, )Tj /T1_1 1 Tf 0.0377 Tc 7.4001 0 0 7.4001 134.33 427.87 Tm (18u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 147.79 427.87 Tm (+ )Tj /T1_0 1 Tf -0.0191 Tc 7.9001 0 0 7.9001 155.6 427.87 Tm (6, )Tj 0.05 Tc 9.8094 0 0 7.9001 163.42 427.87 Tm (... )Tj 0 Tc 7.9001 0 0 7.9001 173.94 427.87 Tm (, )Tj /T1_1 1 Tf 0.0476 Tc 7.4001 0 0 7.4001 177.09 427.87 Tm (24u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 190.99 427.87 Tm (+ )Tj /T1_0 1 Tf -0.0334 Tc 7.9001 0 0 7.9001 198.97 427.87 Tm (5} )Tj 0.05 Tc 8.053 0 0 7.9001 62.45 363.97 Tm (which )Tj 0.0109 Tc 7.9001 0 0 7.9001 86.88 363.97 Tm (is )Tj -0.0204 Tc 8.8 0 0 8.8 95.96 363.97 Tm (Sf, )Tj 0.05 Tc 8.4599 0 0 7.9001 108.63 363.97 Tm (and )Tj -0.0284 Tc 9.2 0 0 9.2 125.44 363.97 Tm ({i )Tj 0 Tc 1.027 0 Td (-)Tj 0.05 Tc 11.2433 0 0 8.6 164.24 363.25 Tm (liE )Tj 0.0087 Tc 8.2 0 0 8.2 196.85 364.15 Tm (is )Tj 0.05 Tc 8.6063 0 0 7.9001 206.08 364.15 Tm (the )Tj /T1_2 1 Tf 0 Tc 7.1 0 0 7.1 66.91 343.63 Tm [({ )92(i )]TJ /T1_1 1 Tf 0.0079 Tc 8.4 0 0 8.4 66.79 334.27 Tm ({i )Tj 0 Tc 0.999 0 Td (-)Tj /T1_2 1 Tf 7.3001 0 0 7.3001 66.9 315.73 Tm [({ )130(i )]TJ 0 -2.54 TD [({ )130(i )]TJ 7.1 0 0 7.1 66.91 269.47 Tm [({ )92(i )]TJ 7.3001 0 0 7.3001 66.72 260.11 Tm ({ )Tj /T1_3 1 Tf 0.518 0 Td (i )Tj /T1_1 1 Tf 0.0079 Tc 8.4 0 0 8.4 66.79 250.93 Tm ({i )Tj 0 Tc 0.999 0 Td (-)Tj /T1_2 1 Tf 7.3001 0 0 7.3001 67.26 241.75 Tm [({ )179(i )]TJ -0.074 -1.282 Td [({ )105(i )]TJ /T1_1 1 Tf 0.0293 Tc 8.4 0 0 8.4 66.61 222.85 Tm ({i )Tj /T1_0 1 Tf 0.0308 Tc 8.2 0 0 8.2 66.45 213.67 Tm ({i )Tj 0 Tc 1.039 0 Td (-)Tj /T1_3 1 Tf 5.6 0 0 5.6 101.97 331.57 Tm (I)Tj 7.3001 0 0 7.3001 106.14 343.99 Tm (i )Tj /T1_0 1 Tf -0.0076 Tc 0.649 0 Td (::::l} )Tj /T1_2 1 Tf 0 Tc -0.66 -1.307 Td (i )Tj 0.05 Tc 9.2292 0 0 7.3001 132.05 334.45 Tm (... )Tj /T1_1 1 Tf 8.1499 0 0 7.4001 142.95 334.45 Tm (,6u} )Tj /T1_2 1 Tf 0 Tc 12.9 0 0 12.9 101.7 315.55 Tm (I )Tj /T1_3 1 Tf 7.3001 0 0 7.3001 106.14 315.55 Tm (i )Tj /T1_0 1 Tf -0.0323 Tc 7.9001 0 0 7.9001 124.27 315.55 Tm (5, )Tj 0.05 Tc 9.8094 0 0 7.9001 132.1 315.55 Tm (... )Tj 0 Tc 7.9001 0 0 7.9001 142.8 315.55 Tm (, )Tj /T1_1 1 Tf 0.05 Tc 7.4524 0 0 7.4001 145.66 315.55 Tm (6u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 155.89 315.55 Tm (+ )Tj /T1_0 1 Tf 0.023 Tc 7.9001 0 0 7.9001 164.11 315.55 Tm (I} )Tj /T1_3 1 Tf 0.0339 Tc 11.7 0 0 11.7 101.86 296.83 Tm (Ii )Tj /T1_1 1 Tf 0.05 Tc 8.0132 0 0 7.4001 110.83 296.83 Tm (=6u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 126.91 296.83 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.7576 0 0 7.9001 135.14 296.83 Tm (2, )Tj /T1_1 1 Tf 0.05 Tc 7.4524 0 0 7.4001 142.42 296.83 Tm (6u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 152.65 296.83 Tm (+ )Tj /T1_0 1 Tf -0.0296 Tc 7.9001 0 0 7.9001 160.47 296.83 Tm (3, )Tj /T1_1 1 Tf 0.0377 Tc 7.4001 0 0 7.4001 167.99 296.83 Tm (12u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 181.81 296.83 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.5884 0 0 7.9001 189.68 296.83 Tm (2} )Tj /T1_1 1 Tf 0 Tc 7.7 0 0 7.7 106.11 269.29 Tm (i )Tj 0.05 Tc 7.817 0 0 7.4001 111.02 269.29 Tm (=12u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 131.05 269.29 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.7176 0 0 7.9001 139.11 269.29 Tm (4, )Tj /T1_1 1 Tf 0.0134 Tc 7.4001 0 0 7.4001 147.11 269.29 Tm (12u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 160.39 269.29 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.8216 0 0 7.9001 168.38 269.29 Tm (6, )Tj 0.05 Tc 9.8094 0 0 7.9001 176.02 269.29 Tm (... )Tj 0 Tc 7.9001 0 0 7.9001 186.54 269.29 Tm (, )Tj /T1_1 1 Tf 0.0377 Tc 7.4001 0 0 7.4001 190.31 269.29 Tm (16u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 203.95 269.29 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.7528 0 0 7.9001 211.83 269.29 Tm (4} )Tj 0.05 Tc 8.0941 0 0 7.9001 111.02 259.93 Tm (=12u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 131.05 259.93 Tm (+ )Tj /T1_0 1 Tf -0.0323 Tc 7.9001 0 0 7.9001 139.21 259.93 Tm (5, )Tj /T1_1 1 Tf 0.0079 Tc 7.7 0 0 7.7 146.92 259.93 Tm (12u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 160.57 259.93 Tm (+ )Tj /T1_0 1 Tf -0.0191 Tc 7.9001 0 0 7.9001 168.22 259.93 Tm (7, )Tj 0.05 Tc 9.8094 0 0 7.9001 176.2 259.93 Tm (... )Tj 0 Tc 7.9001 0 0 7.9001 186.72 259.93 Tm (, )Tj /T1_1 1 Tf 0.0312 Tc 7.7 0 0 7.7 190.12 259.93 Tm (14u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 203.95 259.93 Tm (+ )Tj /T1_0 1 Tf 0.0457 Tc 7.9001 0 0 7.9001 212.35 259.93 Tm (I} )Tj /T1_2 1 Tf 0 Tc 7.3001 0 0 7.3001 106.06 250.75 Tm (i )Tj /T1_1 1 Tf 0.05 Tc 7.738 0 0 7.4001 111.02 250.75 Tm (=14u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 131.05 250.75 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.698 0 0 7.9001 139.23 250.75 Tm (3, )Tj /T1_1 1 Tf 0.0134 Tc 7.4001 0 0 7.4001 147.11 250.75 Tm (14u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 160.57 250.75 Tm (+ )Tj /T1_0 1 Tf -0.0323 Tc 7.9001 0 0 7.9001 168.37 250.75 Tm (5, )Tj 0.05 Tc 15.6092 0 0 7.9001 175.89 250.75 Tm (.. )Tj 0 Tc 7.9001 0 0 7.9001 186.72 250.75 Tm (, )Tj 0.0034 Tc 0.437 0 Td (16u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 203.95 250.75 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.5406 0 0 7.9001 211.95 250.75 Tm (3} )Tj 0.05 Tc 8.0941 0 0 7.9001 111.02 241.39 Tm (=16u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 131.05 241.39 Tm (+ )Tj /T1_0 1 Tf -0.0095 Tc 7.9001 0 0 7.9001 139.03 241.39 Tm (5, )Tj /T1_1 1 Tf 0.0377 Tc 7.4001 0 0 7.4001 146.93 241.39 Tm (16u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 160.57 241.39 Tm (+ )Tj /T1_0 1 Tf -0.0191 Tc 7.9001 0 0 7.9001 168.22 241.39 Tm (7, )Tj 0.05 Tc 9.8094 0 0 7.9001 176.2 241.39 Tm (... )Tj 0 Tc 7.9001 0 0 7.9001 186.72 241.39 Tm (, )Tj /T1_1 1 Tf 0.0499 Tc 7.4001 0 0 7.4001 190.13 241.39 Tm (18u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 203.95 241.39 Tm (+ )Tj /T1_0 1 Tf 0.023 Tc 7.9001 0 0 7.9001 212.35 241.39 Tm (I} )Tj /T1_2 1 Tf 0 Tc 7.3001 0 0 7.3001 106.06 232.39 Tm (i )Tj /T1_0 1 Tf -0.035 Tc 6.2939 0 0 7.9001 110.9 232.39 Tm (::::;:16u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 131.05 232.39 Tm (+ )Tj /T1_0 1 Tf -0.0149 Tc 7.6 0 0 7.6 139.05 232.39 Tm (6, )Tj /T1_1 1 Tf 0.0256 Tc 7.4001 0 0 7.4001 146.93 232.39 Tm (16u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 160.39 232.39 Tm (+ )Tj /T1_0 1 Tf -0.0281 Tc 7.6 0 0 7.6 168.35 232.39 Tm (8, )Tj 0.05 Tc 9.8094 0 0 7.6 176.02 232.39 Tm (... )Tj 0 Tc 7.6 0 0 7.6 186.54 232.39 Tm (, )Tj /T1_1 1 Tf 0.0377 Tc 7.4001 0 0 7.4001 190.13 232.39 Tm (18u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 203.95 232.39 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.3939 0 0 7.6 212 232.39 Tm (2} )Tj /T1_1 1 Tf 0.0232 Tc 7.4001 0 0 7.4001 106.11 222.85 Tm (i::::;:18u+3,18u )Tj /T1_0 1 Tf -0.035 Tc 7.7528 0 0 8.2 168.09 222.85 Tm (4} )Tj /T1_1 1 Tf -0.0346 Tc 7.4001 0 0 7.4001 105.93 213.49 Tm (i::::;:18u+ )Tj 0.05 Tc 8.5085 0 0 7.4001 146.73 213.49 Tm (18u+6, )Tj 10.0659 0 0 7.4001 175.94 213.49 Tm (... )Tj 8.9727 0 0 7.4001 186.51 213.49 Tm (,24u+5} )Tj /T1_0 1 Tf 7.9847 0 0 7.9001 62.27 150.31 Tm (which )Tj 0.0133 Tc 7.6 0 0 7.6 109.2 150.31 Tm (is )Tj /T1_1 1 Tf 0.0212 Tc 9 0 0 9 118.07 150.31 Tm (St. )Tj /T1_0 1 Tf 0.05 Tc 9.811 0 0 7.9001 21.7 113.95 Tm (Theorem )Tj 8.6546 0 0 7.9001 64.03 113.95 Tm (2.5 )Tj /T1_1 1 Tf 9.4986 0 0 8.7 81.89 113.95 Tm (ThereexistsaGBRD\(v,3,2t;Z2t\)!orallt )Tj /T1_0 1 Tf 0.0376 Tc 8.2 0 0 8.2 22.22 103.51 Tm (12\). )Tj 0.05 Tc 8.5556 0 0 7.9001 244.36 364.15 Tm (of )Tj 8.7429 0 0 7.9001 254.14 364.15 Tm (the )Tj -0.035 Tc 7.779 0 0 7.9001 268.65 364.15 Tm (folJloWIllrl )Tj 0.05 Tc 7.9865 0 0 7.9001 305.53 364.15 Tm (sets )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 258.85 342.01 Tm (+ )Tj 0.017 -0.744 Td (+ )Tj /T1_1 1 Tf 0.0079 Tc 7.7 0 0 7.7 275.62 334.27 Tm (12u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 289.09 334.27 Tm (+ )Tj /T1_0 1 Tf -0.0166 Tc 7.7 0 0 7.7 297.09 334.27 Tm (13, )Tj 0.05 Tc 9.5864 0 0 7.7 308.32 334.27 Tm (... )Tj 0 Tc 7.7 0 0 7.7 318.66 334.27 Tm (, )Tj /T1_1 1 Tf 0.0476 Tc 7.4001 0 0 7.4001 321.81 334.27 Tm (24u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 336.07 334.27 Tm (+ )Tj /T1_0 1 Tf -0.0241 Tc 7.7 0 0 7.7 344.07 334.27 Tm (1, )Tj /T1_1 1 Tf 0.05 Tc 10.0659 0 0 7.4001 256.22 325.45 Tm (... )Tj 9.0144 0 0 7.4001 266.79 325.45 Tm (,6u )Tj /T1_0 1 Tf -0.035 Tc 7.3203 0 0 8.2 288.44 325.45 Tm (5} )Tj /T1_3 1 Tf 0 Tc 10.7 0 0 10.7 258.92 315.55 Tm (+ )Tj /T1_1 1 Tf 0.0079 Tc 7.7 0 0 7.7 275.62 315.55 Tm (12u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 289.09 315.55 Tm (+ )Tj -0.0094 Tc 1.878 0 Td (... )Tj 0 Tc 1.008 0 Td (, )Tj /T1_1 1 Tf 0.05 Tc 7.4911 0 0 7.4001 321.63 315.55 Tm (24u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 336.07 315.55 Tm (+ )Tj /T1_0 1 Tf -0.0026 Tc 7.6 0 0 7.6 343.89 315.55 Tm (3, )Tj /T1_3 1 Tf -0.035 Tc 6.7238 0 0 7.4001 248.81 306.91 Tm (9, )Tj 0.05 Tc 9.1635 0 0 7.4001 256.17 306.91 Tm (... )Tj 0 Tc 7.4001 0 0 7.4001 266.89 306.91 Tm (, )Tj /T1_1 1 Tf 0.05 Tc 8.1456 0 0 7.7 270.03 306.91 Tm (6u )Tj /T1_0 1 Tf 0 Tc 7.7 0 0 7.7 281.07 306.91 Tm (-)Tj -0.035 Tc 7.3421 0 0 8.2 288.64 306.91 Tm (3} )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 259.21 295.57 Tm (+ )Tj /T1_0 1 Tf 7.9001 0 0 7.9001 260.6 288.01 Tm (+ )Tj 0.05 Tc 8.6685 0 0 7.9001 286.7 288.01 Tm (+14, )Tj 9.8094 0 0 7.9001 305.98 288.01 Tm (... )Tj 9.0486 0 0 7.9001 316.3 288.01 Tm (,24u+2} )Tj /T1_1 1 Tf 9.426 0 0 7.4001 260.56 278.83 Tm (+6,6u+ )Tj -0.035 Tc 7.599 0 0 8 295.07 278.83 Tm (12, )Tj 0.05 Tc 9.8422 0 0 8 306.09 278.83 Tm (... )Tj 8.0021 0 0 7.4001 316.47 278.83 Tm (,24u} )Tj /T1_3 1 Tf -0.0294 Tc 6.7 0 0 6.7 253.15 269.29 Tm (11, )Tj 0.05 Tc 14.867 0 0 6.7 264.35 269.29 Tm (.. )Tj /T1_1 1 Tf 8.672 0 0 7.4001 275.97 269.29 Tm (,12u+5} )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 259.21 259.93 Tm (+ )Tj /T1_1 1 Tf 0.05 Tc 8.3426 0 0 7.4001 272.01 259.93 Tm (1,12u+17, )Tj 9.3949 0 0 7.4001 312.57 259.93 Tm (... )Tj 9.9142 0 0 7.4001 322.96 259.93 Tm (,18u-1} )Tj 9.3605 0 0 7.4001 255.34 250.57 Tm (+1,6u+7, )Tj 8.2029 0 0 7.4001 300.52 250.57 Tm (.. )Tj 9.3531 0 0 7.4001 307.47 250.57 Tm (,12u+l} )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 259.21 241.39 Tm (+ )Tj /T1_0 1 Tf 0.0259 Tc 7.9001 0 0 7.9001 267.39 241.39 Tm (10, )Tj /T1_1 1 Tf 0.0256 Tc 7.4001 0 0 7.4001 279.59 241.39 Tm (12u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 293.23 241.39 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.6313 0 0 7.9001 301.24 241.39 Tm (16, )Tj 0.05 Tc 9.3635 0 0 7.9001 312.47 241.39 Tm (... )Tj 0 Tc 7.9001 0 0 7.9001 322.8 241.39 Tm (, )Tj /T1_1 1 Tf 0.0377 Tc 7.4001 0 0 7.4001 326.21 241.39 Tm (18u )Tj /T1_0 1 Tf 0 Tc 1.928 0 Td (-)Tj -0.035 Tc 7.5884 0 0 7.9001 348.08 241.39 Tm (2} )Tj -0.0283 Tc 7.7 0 0 7.7 252.99 232.39 Tm (12, )Tj 0.05 Tc 10.0323 0 0 7.7 264.39 232.39 Tm (... )Tj 0 Tc 7.7 0 0 7.7 275.64 232.39 Tm (, )Tj /T1_1 1 Tf -0.0068 Tc 0.395 0 Td (6u )Tj /T1_0 1 Tf 0 Tc 1.339 0 Td (-)Tj -0.035 Tc 7.6355 0 0 7.7 296.37 232.39 Tm (6} )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 259.21 222.49 Tm (+ )Tj /T1_0 1 Tf 0.0367 Tc 7.7 0 0 7.7 267.09 222.49 Tm (4, )Tj /T1_1 1 Tf 0.0481 Tc 7.4001 0 0 7.4001 275.45 222.49 Tm (6u} )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 259.03 213.31 Tm (+ )Tj /T1_0 1 Tf 0.0259 Tc 7.9001 0 0 7.9001 267.21 213.31 Tm (10, )Tj /T1_1 1 Tf 0.0079 Tc 7.7 0 0 7.7 279.4 213.31 Tm (18u )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 292.87 213.31 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.7937 0 0 7.9001 300.87 213.31 Tm (16, )Tj 0.05 Tc 9.5864 0 0 7.9001 312.1 213.31 Tm (... )Tj 0 Tc 7.9001 0 0 7.9001 322.44 213.31 Tm (, )Tj /T1_1 1 Tf 0.0285 Tc 7.7 0 0 7.7 325.59 213.31 Tm (24u )Tj /T1_0 1 Tf 0 Tc 1.886 0 Td (-)Tj -0.035 Tc 7.783 0 0 7.9001 347.71 213.31 Tm (2} )Tj 0.0201 Tc 7.4001 0 0 7.4001 265.6 203.59 Tm ('" )Tj /T1_1 1 Tf 0.05 Tc 8.0583 0 0 7.4001 277.05 203.59 Tm (,6u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 289.99 203.59 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.1993 0 0 8.2 297.86 203.59 Tm (2} )Tj 0.05 Tc 8.8228 0 0 7.9001 264.56 194.77 Tm (+4,4,10, )Tj 9.5864 0 0 7.9001 299.14 194.77 Tm (... )Tj 9.7522 0 0 7.9001 309.45 194.77 Tm (,12u-)Tj -0.035 Tc 7.5884 0 0 7.9001 334.4 194.77 Tm (2} )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 264.61 185.59 Tm (+ )Tj /T1_0 1 Tf -0.0311 Tc 7.9001 0 0 7.9001 273.15 185.59 Tm (11, )Tj /T1_1 1 Tf 0.0256 Tc 7.4001 0 0 7.4001 284.63 185.59 Tm (18u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 298.27 185.59 Tm (+ )Tj /T1_0 1 Tf -0.0311 Tc 7.9001 0 0 7.9001 306.27 185.59 Tm (17, )Tj 0.05 Tc 9.3635 0 0 7.9001 317.51 185.59 Tm (... )Tj 0 Tc 7.9001 0 0 7.9001 327.66 185.59 Tm (, )Tj /T1_1 1 Tf 0.0285 Tc 7.7 0 0 7.7 330.99 185.59 Tm (24u )Tj /T1_0 1 Tf 0 Tc 1.862 0 Td (-)Tj 0.0457 Tc 7.9001 0 0 7.9001 353.65 185.59 Tm (I} )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 260.29 176.23 Tm (+ )Tj /T1_0 1 Tf 0.0496 Tc 7.9001 0 0 7.9001 268.29 176.23 Tm (9, )Tj /T1_1 1 Tf 0.0261 Tc 5.6 0 0 5.6 276.74 176.23 Tm (67t )Tj /T1_2 1 Tf 0 Tc 10.4 0 0 10.4 286.39 176.23 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.7937 0 0 7.9001 294.57 176.23 Tm (15, )Tj 0.05 Tc 9.5864 0 0 7.9001 305.8 176.23 Tm (... )Tj 0 Tc 7.9001 0 0 7.9001 316.14 176.23 Tm (, )Tj /T1_1 1 Tf 0.0256 Tc 7.4001 0 0 7.4001 319.55 176.23 Tm (12u )Tj /T1_0 1 Tf 0 Tc 1.855 0 Td (-)Tj -0.035 Tc 7.739 0 0 7.9001 341.19 176.23 Tm (3} )Tj /T1_3 1 Tf 0 Tc 11 0 0 11 260.17 166.51 Tm (+ )Tj /T1_1 1 Tf 0.0134 Tc 7.4001 0 0 7.4001 277.25 166.51 Tm (18u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 290.53 166.51 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.5182 0 0 7.6 298.16 166.51 Tm (5} )Tj /T1_2 1 Tf 0 Tc 8.7 0 0 8.7 339.58 131.77 Tm (o )Tj /T1_1 1 Tf 0.0406 Tc -9.349 -2.09 Td (and )Tj -0.026 Tc 2.007 0 Td (all )Tj 0 Tc 1.284 0 Td (v )Tj /T1_0 1 Tf -0.035 Tc 5.0019 0 0 9.1 293.56 113.59 Tm (== )Tj 0 Tc 8.2 0 0 8.2 302.48 113.59 Tm (1 )Tj /T1_1 1 Tf 0.0208 Tc 8.7 0 0 8.7 309.53 113.59 Tm (or )Tj /T1_0 1 Tf 0 Tc 8.2 0 0 8.2 319.77 113.59 Tm (9 )Tj /T1_1 1 Tf 0.0076 Tc 8.7 0 0 8.7 327.25 113.59 Tm (\(mod )Tj /T1_0 1 Tf 0.05 Tc 9.4819 0 0 7.9001 21.74 77.77 Tm (Proof: )Tj 0.0475 Tc 7.9001 0 0 7.9001 54.5 77.77 Tm (Let )Tj /T1_2 1 Tf 0.05 Tc 4.44 0 0 4.1 70.06 77.77 Tm (1\) )Tj /T1_0 1 Tf 8.3331 0 0 7.9001 105.1 77.41 Tm (the )Tj 8.1789 0 0 7.9001 119.98 77.41 Tm (above )Tj 8.1232 0 0 7.9001 145 77.41 Tm (condition. )Tj 8.2998 0 0 7.9001 187.7 77.41 Tm (From )Tj -0.0045 Tc 7.9001 0 0 7.9001 211.13 77.41 Tm ([3], )Tj /T1_1 1 Tf 0.05 Tc 9.3238 0 0 8.7 233.27 77.41 Tm (GBRD\(v,3,2; )Tj /T1_0 1 Tf 7.9566 0 0 7.9001 305.2 77.41 Tm (exists, )Tj 8.5774 0 0 7.9001 331.65 77.41 Tm (and )Tj 8.7429 0 0 7.9001 21.76 66.96 Tm (the )Tj 8.0435 0 0 7.9001 36.82 66.96 Tm (existence )Tj 8.3469 0 0 7.9001 73.72 66.96 Tm (of )Tj 0 Tc 7.9001 0 0 7.9001 83.8 66.96 Tm (a )Tj 0.0338 Tc -7.857 -1.32 Td (2.3 )Tj 0.05 Tc 8.4599 0 0 7.9001 35.91 56.53 Tm (and )Tj 0.0379 Tc 7.9001 0 0 7.9001 52.69 56.53 Tm (2.4. )Tj 0.05 Tc 8.8085 0 0 7.9001 127.88 66.78 Tm (3,1\) )Tj 0.0337 Tc 7.9001 0 0 7.9001 146.28 66.78 Tm (is )Tj 0.0057 Tc 1.168 0 Td (well )Tj 0.05 Tc 8.047 0 0 7.9001 172.96 66.78 Tm (known. )Tj 8.7991 0 0 7.9001 204.05 66.78 Tm (The )Tj 8.0934 0 0 7.9001 221.93 66.78 Tm (result )Tj 8.2885 0 0 7.9001 246.22 66.78 Tm (then )Tj 0.0326 Tc 7.9001 0 0 7.9001 265.41 66.78 Tm (follows )Tj 0.05 Tc 7.9254 0 0 7.9001 294.03 66.78 Tm (from )Tj 8.1757 0 0 7.9001 314.78 66.78 Tm (Lemmas )Tj 0 Tc 10.3 0 0 10.3 339.56 56.35 Tm (o )Tj -0.0066 Tc 8.2 0 0 8.2 181.16 33.13 Tm (11 )Tj ET endstream endobj 161 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 49302/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream (j *ZKT~@TG-Q *ZKr>@TG 0b GZ?-Q (j (j **Х-QAr? 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0 0 7.8001 116.92 499.87 Tm (3u+5, )Tj 10.0659 0 0 7.8001 142.46 499.87 Tm (... )Tj 8.9917 0 0 7.8001 153.21 499.87 Tm (,4u+ )Tj /T1_0 1 Tf -0.035 Tc 7.4262 0 0 7.9001 174.52 499.87 Tm (1} )Tj 0.0195 Tc 8.3 0 0 8.3 37.43 479.89 Tm (which )Tj 0.0476 Tc 2.919 0 Td (again )Tj /T1_2 1 Tf 0.0384 Tc 8.4 0 0 8.4 93.41 479.89 Tm (St. )Tj /T1_0 1 Tf 0.0349 Tc 7.9001 0 0 7.9001 19.17 462.43 Tm (\(iii\) )Tj /T1_2 1 Tf 0 Tc 8.8 0 0 8.8 37.34 462.43 Tm (t )Tj /T1_0 1 Tf -0.035 Tc 5.0019 0 0 9.1 43.18 462.43 Tm (== )Tj 0 Tc 8.3 0 0 8.3 51.97 462.43 Tm (2 )Tj 0.05 Tc 8.5137 0 0 8.3 59.12 462.43 Tm (\(mod )Tj 0.0281 Tc 8.3 0 0 8.3 81.51 462.43 Tm (4\) )Tj 0.05 Tc 9.1419 0 0 8.3 37.58 448.75 Tm (Put )Tj /T1_1 1 Tf 0 Tc 6.9001 0 0 6.9001 54.24 448.75 Tm (u )Tj /C0_0 1 Tf 3.4201 0 0 7.7401 71.29 448.75 Tm <007E002800740020>Tj /T1_3 1 Tf 12.2 0 0 12.2 84.4 448.75 Tm (+ )Tj /T1_0 1 Tf 0.05 Tc 8.4599 0 0 8.3 105.21 448.75 Tm (and )Tj 8.3506 0 0 8.3 121.84 448.75 Tm (take )Tj 10.0323 0 0 7.8001 185.91 527.59 Tm (... )Tj /T1_2 1 Tf 8.3315 0 0 7.8001 196.77 527.59 Tm (,3u )Tj /T1_3 1 Tf -0.035 Tc 6.1579 0 0 11.6 209.96 527.59 Tm (+-)Tj /T1_0 1 Tf 7.4262 0 0 7.9001 217.9 527.59 Tm (1} )Tj /T1_2 1 Tf 0.0299 Tc 8.5 0 0 8.5 93.17 431.11 Tm (4u )Tj /T1_0 1 Tf 0 Tc 1.352 0 Td (-)Tj /T1_3 1 Tf 8 0 0 8 112.71 431.11 Tm [(i )-162(-)-677(5 )]TJ /T1_2 1 Tf 8.5 0 0 8.5 93.35 420.49 Tm (u )Tj /T1_3 1 Tf 7.8001 0 0 7.8001 108.65 420.49 Tm (1 )Tj 8 0 0 8 139 430.75 Tm [(\( )207(i )]TJ 0 -1.282 TD [(\( )207(i )]TJ /T1_2 1 Tf -0.0294 Tc 8.5 0 0 8.5 156.81 430.93 Tm (1, )Tj 0.05 Tc 11.408 0 0 8.5 164.77 430.93 Tm (... )Tj 12.4383 0 0 8.5 176.8 430.93 Tm (,u-1\) )Tj -0.035 Tc 9.4151 0 0 11.5 156.52 420.31 Tm (u\) )Tj /T1_0 1 Tf 0.0148 Tc 8.2 0 0 8.2 247.17 546.49 Tm ({3,5, )Tj 0.05 Tc 17.7377 0 0 8.2 265.67 546.49 Tm (.. )Tj /T1_2 1 Tf 7.9218 0 0 7.8001 277.77 546.49 Tm (,2u )Tj /T1_0 1 Tf 10.245 0 0 8.2 290.58 546.49 Tm (-1} )Tj 0.0223 Tc 8.2 0 0 8.2 247.17 537.12 Tm ({I} )Tj /T1_2 1 Tf 0.015 Tc 7.8001 0 0 7.8001 247.34 527.59 Tm ({2u )Tj /T1_0 1 Tf 0 Tc 10 0 0 10 261.13 527.59 Tm (+ )Tj /T1_2 1 Tf -0.0167 Tc 7.8001 0 0 7.8001 277.17 527.59 Tm (2u )Tj /T1_0 1 Tf 0 Tc 10 0 0 10 287.23 527.59 Tm (+ )Tj -0.005 Tc 7.4001 0 0 7.4001 294.81 527.59 Tm (4, )Tj 0.05 Tc 9.5864 0 0 7.4001 302.38 527.59 Tm (... )Tj /T1_2 1 Tf 0.0492 Tc 7.8001 0 0 7.8001 312.87 527.59 Tm (,4u, )Tj /T1_0 1 Tf 0.05 Tc 7.6145 0 0 7.4001 247.28 518.59 Tm (2,4, )Tj 11.3521 0 0 7.4001 268.68 518.59 Tm (., )Tj /T1_2 1 Tf 0.0345 Tc 7.8001 0 0 7.8001 276.63 518.59 Tm (2u} )Tj /T1_1 1 Tf 0 Tc 10.2 0 0 10.2 261.09 509.05 Tm (+ )Tj /T1_2 1 Tf -0.0167 Tc 7.8001 0 0 7.8001 277.17 509.05 Tm (2u )Tj /T1_3 1 Tf 0 Tc 10.7 0 0 10.7 287.11 509.05 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.5642 0 0 7.8001 294.94 509.05 Tm (9, )Tj 0.05 Tc 9.3635 0 0 7.8001 302.39 509.05 Tm (... )Tj 0 Tc 7.8001 0 0 7.8001 312.72 509.05 Tm (, )Tj /T1_2 1 Tf 0.0057 Tc 0.376 0 Td (4u )Tj /T1_3 1 Tf 0 Tc 10.7 0 0 10.7 325.45 509.05 Tm (+ )Tj /T1_0 1 Tf 0.0335 Tc 7.8001 0 0 7.8001 334.21 509.05 Tm (I} )Tj /T1_1 1 Tf 0 Tc 10.2 0 0 10.2 260.91 500.05 Tm (+ )Tj /T1_2 1 Tf -0.0167 Tc 7.8001 0 0 7.8001 277.17 500.05 Tm (2u )Tj /T1_3 1 Tf 0 Tc 10.2 0 0 10.2 287.11 500.05 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.5609 0 0 7.8001 294.94 500.05 Tm (7, )Tj 0.05 Tc 9.5864 0 0 7.8001 302.38 500.05 Tm (... )Tj 0 Tc 7.8001 0 0 7.8001 312.72 500.05 Tm (, )Tj /T1_2 1 Tf -0.035 Tc 7.7555 0 0 7.8001 315.83 500.05 Tm (4u )Tj /T1_0 1 Tf 0 Tc 7.8001 0 0 7.8001 325.71 500.05 Tm (-)Tj 0.05 Tc 7.8603 0 0 7.8001 334.21 500.05 Tm (I} )Tj /T1_2 1 Tf 11.6654 0 0 8.5 93.14 410.23 Tm (4u-)Tj /T1_0 1 Tf -0.035 Tc 7.1466 0 0 8.1 55.55 399.43 Tm (7r2\( )Tj 0.05 Tc 8.3871 0 0 8.2 67.61 399.43 Tm (i\) )Tj -0.035 Tc 5.6702 0 0 8.2 76.18 399.43 Tm (:::: )Tj /T1_2 1 Tf 0 Tc 8.5 0 0 8.5 93.53 399.43 Tm (u )Tj /T1_0 1 Tf 0.05 Tc 14.0396 0 0 9.1 117.73 409.69 Tm (-4 )Tj /T1_3 1 Tf 0 Tc 8 0 0 8 139 409.87 Tm [(\( )207(i )]TJ 0 -1.305 TD [(\( )207(i )]TJ /T1_2 1 Tf 8.5 0 0 8.5 156.71 409.87 Tm (u )Tj /T1_3 1 Tf 12.2 0 0 12.2 163.42 409.87 Tm (+ )Tj /T1_0 1 Tf -0.0063 Tc 8.3 0 0 8.3 172.33 409.87 Tm (1, )Tj /T1_2 1 Tf 0 Tc 8.5 0 0 8.5 180.29 409.87 Tm (u )Tj /T1_3 1 Tf 12.2 0 0 12.2 187.18 409.87 Tm (+ )Tj /T1_0 1 Tf 0.0279 Tc 8.3 0 0 8.3 195.61 409.87 Tm (2, )Tj 0.05 Tc 10.9241 0 0 8.3 204.25 409.87 Tm (... )Tj 0 Tc 8.3 0 0 8.3 215.87 409.87 Tm (, )Tj /T1_2 1 Tf 0.0094 Tc 8.5 0 0 8.5 219.21 409.87 Tm (2u )Tj /T1_0 1 Tf 0 Tc 1.347 0 Td (-)Tj 0.0242 Tc 8.3 0 0 8.3 238.58 409.87 Tm (3, )Tj /T1_2 1 Tf 0.0094 Tc 8.5 0 0 8.5 246.75 409.87 Tm (2u )Tj /T1_0 1 Tf 0 Tc 1.326 0 Td (-)Tj 0.05 Tc 8.8938 0 0 8.3 266.45 409.87 Tm (1, )Tj 10.4782 0 0 8.3 275.72 409.87 Tm (... )Tj 0 Tc 8.3 0 0 8.3 286.97 409.87 Tm (, )Tj /T1_2 1 Tf -0.0022 Tc 8.5 0 0 8.5 290.44 409.87 Tm (3u )Tj /T1_0 1 Tf 0 Tc 1.332 0 Td (-)Tj 0.0253 Tc 8.3 0 0 8.3 309.67 409.87 Tm (5\) )Tj /T1_2 1 Tf 0.0402 Tc 8.5 0 0 8.5 156.52 399.61 Tm (3u )Tj /T1_0 1 Tf 0.0082 Tc 2.335 0 Td (4\) )Tj /T1_2 1 Tf 0.05 Tc 13.067 0 0 8.5 93.49 389.35 Tm (u-3 )Tj /T1_3 1 Tf 0 Tc 8 0 0 8 139 388.99 Tm [(\( )207(i )]TJ /T1_2 1 Tf 0.019 Tc 8.5 0 0 8.5 156.7 389.17 Tm (3u )Tj /T1_0 1 Tf 0 Tc 1.332 0 Td (-)Tj 0.0086 Tc 0.995 0 Td (3\) )Tj /T1_2 1 Tf 0.0299 Tc -9.801 -1.249 Td (4u )Tj 0 Tc 8.8 0 0 8.8 112.93 378.55 Tm (i )Tj /T1_0 1 Tf 7.9001 0 0 7.9001 126.28 378.37 Tm (7 )Tj /T1_2 1 Tf 0.0087 Tc 8.5 0 0 8.5 93.35 368.29 Tm (4u )Tj /T1_0 1 Tf 0 Tc 1.352 0 Td (-)Tj /T1_3 1 Tf 8 0 0 8 112.71 368.29 Tm [(i )-162(-)]TJ /T1_0 1 Tf 8.4 0 0 8.4 126.26 368.29 Tm (3 )Tj /T1_3 1 Tf 8 0 0 8 139 378.37 Tm [(\( )185(i )]TJ /T1_0 1 Tf 8.2 0 0 8.2 139.04 367.93 Tm [(\( )184(i )]TJ /T1_2 1 Tf 0.0402 Tc 8.5 0 0 8.5 156.52 378.55 Tm (3u )Tj 0.05 Tc 8.8111 0 0 8.5 176.54 378.55 Tm (2,3u, )Tj 10.9607 0 0 8.5 198.25 378.55 Tm (... )Tj 9.0144 0 0 8.5 209.73 378.55 Tm (,4u )Tj -0.0169 Tc 8.5 0 0 8.5 232.58 378.55 Tm (6\) )Tj 0.05 Tc 11.4643 0 0 8.5 156.49 367.93 Tm (3u-l,3u+1, )Tj 10.737 0 0 8.5 213.02 367.93 Tm (... )Tj 9.2876 0 0 8.5 224.31 367.93 Tm (,4u )Tj -0.0112 Tc 8.5 0 0 8.5 247.23 367.93 Tm (5\) )Tj /T1_0 1 Tf 0.05 Tc 8.5615 0 0 8.3 37.73 347.23 Tm (Then )Tj 6.1294 0 0 5.7 60.06 347.23 Tm (7r2\( )Tj /T1_2 1 Tf 8.5539 0 0 8.4 72.17 347.23 Tm (St\) )Tj /T1_0 1 Tf 8.6063 0 0 8.3 94.48 347.23 Tm (the )Tj 0.0381 Tc 8.3 0 0 8.3 109.26 347.23 Tm (union )Tj 0.05 Tc 8.3469 0 0 8.3 132.76 347.23 Tm (of )Tj 8.6063 0 0 8.3 142.72 347.23 Tm (the )Tj 8.3193 0 0 8.3 193.56 347.23 Tm (sets )Tj -0.035 Tc 7.6855 0 0 8.2 48.47 319.69 Tm ({7r2\(i\) )Tj /T1_3 1 Tf 0 Tc 14.3 0 0 14.3 71.42 319.69 Tm (I )Tj /T1_1 1 Tf 7.3001 0 0 7.3001 76.08 319.69 Tm (i )Tj /T1_3 1 Tf 0.0379 Tc 7.9001 0 0 7.9001 80.51 319.69 Tm (=1, )Tj 0.05 Tc 8.4991 0 0 7.9001 97.33 319.69 Tm (.. )Tj 0 Tc 7.9001 0 0 7.9001 104.57 319.69 Tm (, )Tj /T1_2 1 Tf 7.8001 0 0 7.8001 107.76 319.69 Tm (u )Tj /T1_3 1 Tf 0.0189 Tc 7.9001 0 0 7.9001 121.97 319.69 Tm (1} )Tj /T1_0 1 Tf -0.035 Tc 7.6855 0 0 8.2 48.47 311.23 Tm ({7r2\(i\) )Tj /T1_3 1 Tf 0 Tc 7.3001 0 0 7.3001 75.82 311.23 Tm (i )Tj /T1_2 1 Tf 0.05 Tc 8.7588 0 0 7.8001 92.82 311.23 Tm (+1, )Tj 9.6185 0 0 7.8001 108.27 311.23 Tm (... )Tj 10.6145 0 0 7.8001 118.66 311.23 Tm (,2u-3,2u-1, )Tj 9.8422 0 0 7.8001 172.71 311.23 Tm (... )Tj 10.4671 0 0 7.8001 183.28 311.23 Tm (,3u-5} )Tj 9.531 0 0 7.8001 234.17 320.41 Tm ({4u-6,4u )Tj 8.1396 0 0 7.8001 274.44 320.41 Tm (--7, )Tj 9.6185 0 0 7.8001 289.71 320.41 Tm (... )Tj 10.2671 0 0 7.8001 299.92 320.41 Tm (,3u-4} )Tj 9.7461 0 0 7.8001 234.34 311.05 Tm ({3u-)Tj 8.1258 0 0 7.8001 255.7 311.05 Tm (5,3u )Tj /T1_3 1 Tf 7.7268 0 0 7.4001 274.43 311.05 Tm (--6, )Tj 8.6139 0 0 7.4001 289.57 311.05 Tm (... )Tj /T1_2 1 Tf 7.9218 0 0 7.8001 300.09 311.05 Tm (,2u )Tj 10.97 0 0 7.8001 313.12 311.05 Tm (-1, )Tj 10.8155 0 0 7.8001 244.54 301.69 Tm (-3, )Tj 8.9162 0 0 7.8001 259.65 301.69 Tm (.. )Tj 9.9001 0 0 7.8001 270.22 301.69 Tm (,u+1} )Tj /T1_3 1 Tf 0 Tc 13.9 0 0 13.9 71.26 271.09 Tm (I)Tj /T1_1 1 Tf 0.399 1.502 Td (. )Tj /T1_2 1 Tf 0.05 Tc 9.7544 0 0 7.8001 96.59 291.97 Tm (-2,?u, )Tj 9.8422 0 0 7.8001 123.93 291.97 Tm (... )Tj 10.3338 0 0 7.8001 134.5 291.97 Tm (,4u-6} )Tj /T1_0 1 Tf 0 Tc 7.8001 0 0 7.8001 75.92 283.33 Tm [(z )-1976(-)]TJ -0.035 Tc 7.5513 0 0 7.8001 104.68 283.33 Tm (1, )Tj /T1_2 1 Tf 0.016 Tc 7.8001 0 0 7.8001 111.71 283.33 Tm (3u )Tj /T1_3 1 Tf 0 Tc 10.7 0 0 10.7 121.87 283.33 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.2717 0 0 7.8001 130.07 283.33 Tm (1, )Tj 0.05 Tc 9.5864 0 0 7.8001 137.5 283.33 Tm (... )Tj 0 Tc 7.8001 0 0 7.8001 148.02 283.33 Tm (, )Tj /T1_2 1 Tf 0.0288 Tc 0.353 0 Td (4u )Tj /T1_0 1 Tf 0 Tc 2.326 0 Td [(5 )208(} )]TJ /T1_2 1 Tf 8.1 0 0 8.1 76.04 273.97 Tm (i )Tj 0.05 Tc 8.0289 0 0 7.8001 80.59 273.97 Tm (=u, )Tj -0.0071 Tc 7.8001 0 0 7.8001 94.61 273.97 Tm (3u )Tj /T1_0 1 Tf 0 Tc 1.313 0 Td (-)Tj /T1_2 1 Tf 0.016 Tc 1.895 0 Td (3u )Tj /T1_0 1 Tf 0 Tc 1.359 0 Td (-)Tj -0.035 Tc 7.5406 0 0 7.8001 137.79 273.97 Tm (3} )Tj /T1_2 1 Tf 0.0453 Tc 7.8001 0 0 7.8001 234.38 292.33 Tm ({u )Tj 0.05 Tc 8.5079 0 0 7.8001 251.73 292.33 Tm (5,u )Tj /T1_1 1 Tf -0.035 Tc 6.9849 0 0 7.2 274.07 292.33 Tm (7, )Tj 0.05 Tc 8.9599 0 0 7.2 281.73 292.33 Tm (... )Tj /T1_2 1 Tf 8.303 0 0 7.8001 292.17 292.33 Tm (,1,4u )Tj /T1_0 1 Tf -0.035 Tc 7.716 0 0 7.8001 319.93 292.33 Tm (5} )Tj /T1_2 1 Tf 0.05 Tc 10.4689 0 0 7.8001 234.33 283.15 Tm ({u-2,u )Tj /T1_0 1 Tf -0.035 Tc 7.7176 0 0 7.8001 274.11 283.15 Tm (4, )Tj 0.05 Tc 9.8094 0 0 7.8001 281.68 283.15 Tm (... )Tj 8.0455 0 0 7.8001 292.02 283.15 Tm (,4,2} )Tj /T1_2 1 Tf 0.0222 Tc 7.8001 0 0 7.8001 234.56 273.79 Tm ({u )Tj 0.05 Tc 8.8457 0 0 7.8001 252.2 273.79 Tm (1,u,u )Tj /T1_0 1 Tf 10.245 0 0 8.4 274.74 273.79 Tm (-3} )Tj 0.0141 Tc 8.3 0 0 8.3 37.79 252.91 Tm (which )Tj -0.0209 Tc 2.877 0 Td (is )Tj /T1_2 1 Tf 0.0054 Tc 9.1 0 0 9.1 71.09 252.91 Tm (St, )Tj /T1_0 1 Tf 0.05 Tc 8.3424 0 0 8.3 83.98 252.91 Tm (and )Tj -0.0088 Tc 9.2 0 0 9.2 100.42 252.91 Tm ({i )Tj /T1_2 1 Tf -0.035 Tc 7.424 0 0 9 117.83 252.91 Tm (7rz\( )Tj /T1_0 1 Tf 0.0198 Tc 8.8 0 0 8.8 130.07 252.91 Tm (i\) )Tj /T1_3 1 Tf 0 Tc 11.7 0 0 11.7 138.82 252.91 Tm (I )Tj 7.6 0 0 7.6 149.04 252.91 Tm (E )Tj /T1_2 1 Tf 0.05 Tc 10.5234 0 0 9.1 156.94 252.91 Tm (Sd )Tj /T1_0 1 Tf 8.8795 0 0 8.3 180.7 252.91 Tm (the )Tj 0.0381 Tc 8.3 0 0 8.3 195.66 252.91 Tm (union )Tj 0.05 Tc 8.3469 0 0 8.3 219.34 252.91 Tm (of )Tj 8.7429 0 0 8.3 229.12 252.91 Tm (the )Tj 0.0368 Tc 8.3 0 0 8.3 280.5 252.91 Tm (sets )Tj 0.0308 Tc 8.2 0 0 8.2 41.97 226.27 Tm ({i )Tj 0 Tc 1.061 0 Td (-)Tj 0.0308 Tc -1.061 -1.12 Td ({i )Tj 0 Tc 1.039 0 Td (-)Tj /T1_3 1 Tf 14.3 0 0 14.3 77.36 215.47 Tm (I )Tj /C0_0 1 Tf 2.1601 0 0 17.6401 81.72 215.47 Tm <007E0020>Tj /T1_1 1 Tf -0.035 Tc 6.9049 0 0 7.3001 99.6 226.27 Tm (2, )Tj 0.05 Tc 8.5526 0 0 7.3001 107.68 226.27 Tm (... )Tj /T1_2 1 Tf 9.5227 0 0 7.8001 117.93 226.27 Tm (,u--1} )Tj 8.8805 0 0 7.8001 98.4 216.73 Tm (+1, )Tj 9.8422 0 0 7.8001 114.03 216.73 Tm (... )Tj 9.9099 0 0 7.8001 124.6 216.73 Tm (,2u-3,2u )Tj /T1_0 1 Tf -0.0098 Tc 7.8001 0 0 7.8001 178.83 216.19 Tm ('" )Tj /T1_2 1 Tf 0.05 Tc 8.1949 0 0 7.8001 189.39 216.19 Tm (,3u )Tj /T1_0 1 Tf 0.0088 Tc 8.2 0 0 8.2 41.97 198.37 Tm ({i )Tj 0 Tc 1.039 0 Td (-)Tj 0.0088 Tc -1.039 -1.143 Td ({i )Tj 0 Tc 1.039 0 Td (-)Tj 0.0308 Tc -1.061 -1.14 Td ({i )Tj 0 Tc 1.039 0 Td (-)Tj /T1_3 1 Tf 14.6 0 0 14.6 77.18 197.65 Tm (I )Tj /C0_0 1 Tf 2.1601 0 0 7.5601 81.72 197.65 Tm <007E0020>Tj /T1_2 1 Tf 0.039 Tc 7.8001 0 0 7.8001 86.54 197.65 Tm (=3u )Tj /T1_0 1 Tf 0 Tc 2.07 0 Td (-)Tj -0.0257 Tc 7.4001 0 0 7.4001 110.12 197.65 Tm (2, )Tj /T1_2 1 Tf 0.033 Tc 7.8001 0 0 7.8001 117.47 197.65 Tm (3u, )Tj /T1_0 1 Tf 0.05 Tc 9.5864 0 0 7.8001 129.76 197.65 Tm (... )Tj /T1_2 1 Tf 8.1949 0 0 7.8001 140.25 197.65 Tm (,4u )Tj /T1_0 1 Tf -0.0301 Tc 7.4001 0 0 7.4001 161.19 197.65 Tm (6} )Tj /T1_3 1 Tf 0 Tc 14.6 0 0 14.6 77.18 176.59 Tm (I )Tj /C0_0 1 Tf 1.98 0 0 6.1201 81.72 188.83 Tm <007E0020>Tj /T1_2 1 Tf -0.035 Tc 6.2881 0 0 7.8001 86.47 188.83 Tm (::::3u )Tj /T1_0 1 Tf 0 Tc 7.8001 0 0 7.8001 102.51 188.83 Tm (-)Tj -0.035 Tc 7.5513 0 0 7.8001 110.26 188.83 Tm (1, )Tj /T1_2 1 Tf 0.0391 Tc 7.8001 0 0 7.8001 117.47 188.83 Tm (3u )Tj /T1_3 1 Tf 0 Tc 10.2 0 0 10.2 127.63 188.83 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.5513 0 0 7.8001 135.64 188.83 Tm (1, )Tj 0.05 Tc 9.8094 0 0 7.8001 143.08 188.83 Tm (... )Tj 0 Tc 7.8001 0 0 7.8001 153.6 188.83 Tm (, )Tj /T1_2 1 Tf 0.0057 Tc 0.376 0 Td (4u )Tj /T1_0 1 Tf 0 Tc 1.359 0 Td (-)Tj -0.035 Tc 7.5609 0 0 7.8001 174.7 188.83 Tm (7, )Tj /T1_2 1 Tf 0.05 Tc 8.292 0 0 7.8001 181.91 188.83 Tm (4u"-)Tj /T1_0 1 Tf -0.035 Tc 7.716 0 0 7.8001 200.41 188.83 Tm (5} )Tj 0 Tc 7.4001 0 0 7.4001 81.68 179.65 Tm (z )Tj /T1_2 1 Tf -0.035 Tc 7.5904 0 0 7.8001 86.45 179.65 Tm (::::u,3u )Tj /T1_0 1 Tf 6.8622 0 0 7.8001 110.44 179.65 Tm (-" )Tj /T1_2 1 Tf 0.05 Tc 8.11 0 0 7.8001 117.83 179.65 Tm (4,3u )Tj /T1_0 1 Tf 0 Tc 7.8001 0 0 7.8001 135.81 179.65 Tm (-)Tj -0.035 Tc 7.739 0 0 7.9001 143.37 179.65 Tm (3} )Tj 0.0195 Tc 8.3 0 0 8.3 37.25 159.31 Tm (which )Tj 0.0476 Tc 2.941 0 Td (again )Tj 0.0109 Tc 7.9001 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&߆o÷ɷmm6|ۯ\t;]~~߅ww;]~~߅ww;]~~߅ww;]~~߅w߁w;;|C߁w;;|C߁w;;|C߁w;;|C߉w;;NN|'S߉w;;NN|'S߉w;;NN|'S߉w;;NN|'S ߅w]..|K ߅w]..|K ߅w]..|K ߅w]..|?|x>stream q 403.1999969 0 0 336.9600067 0 239.0399933 cm /Im0 Do Q q 403.1999969 0 0 239.0399933 0 0 cm /Im1 Do Q BT /T1_0 1 Tf 0.05 Tc 3 Tr 9.3502 0 0 8.2 37.04 569.17 Tm (Proof: )Tj 0.009 Tc 8.3 0 0 8.3 84.7 569.53 Tm (consld,er )Tj /C0_0 1 Tf 0 Tc 2.2838 0 0 6.1201 119.35 569.53 Tm <0030007E0027004900590055002C0027003C004800220022007E002C002E00720020>Tj /T1_0 1 Tf 0.05 Tc 8.6063 0 0 8.3 160.9 569.53 Tm (the )Tj 0.031 Tc 8.3 0 0 8.3 175.95 569.53 Tm (four )Tj -0.0309 Tc 4.794 0 Td (ac:cordlnlF )Tj 0.05 Tc 8.9493 0 0 8.3 254.86 569.53 Tm (to )Tj 9.0161 0 0 8.3 265.84 569.53 Tm (the )Tj 8.4133 0 0 8.3 281.62 569.53 Tm (congruency )Tj 0.0494 Tc 8.3 0 0 8.3 328.66 569.53 Tm (modulo )Tj 0 Tc 3.751 0 Td (4 )Tj -0.035 Tc 5.814 0 0 5.9001 109.56 559.09 Tm (7r1 )Tj 0.05 Tc 8.3113 0 0 8.3 130.66 559.09 Tm (taken )Tj 9.1676 0 0 8.3 154.42 559.09 Tm (to )Tj 8.7859 0 0 8.3 165.61 559.09 Tm (be )Tj 8.6063 0 0 8.3 178 559.09 Tm (the )Tj 0.034 Tc 8.3 0 0 8.3 193.07 559.09 Tm (identity, )Tj 0.05 Tc 8.4599 0 0 8.3 226.71 559.09 Tm (and )Tj 8.3687 0 0 8.3 257.13 559.09 Tm (exhibit )Tj 8.4916 0 0 8.3 295.48 559.09 Tm (construction )Tj 0.0255 Tc 8.3 0 0 8.3 345.87 559.09 Tm (for )Tj 0.05 Tc 8.4369 0 0 8.3 37.09 548.29 Tm (particular )Tj 9.084 0 0 8.3 118.96 548.65 Tm (that )Tj 8.5069 0 0 8.3 137.26 548.65 Tm (operations )Tj 8.3949 0 0 8.3 179.92 548.65 Tm (are )Tj 0.032 Tc 8.3 0 0 8.3 194.02 548.65 Tm (modulo )Tj 0.0094 Tc 8.4 0 0 8.4 45.08 530.83 Tm (\(i\) )Tj 0 Tc 8.2 0 0 8.2 73 530.83 Tm (0 )Tj 0.05 Tc 8.9153 0 0 8.2 80.54 530.83 Tm (\(mod )Tj 0.0164 Tc 8.2 0 0 8.2 104.37 530.83 Tm (4\) )Tj -0.035 Tc 9.1963 0 0 9.2 43.63 237.07 Tm (\(ii\) )Tj 0.05 Tc 9.2689 0 0 8.3 58.46 517.51 Tm (Put )Tj /T1_1 1 Tf 0 Tc 6.9001 0 0 6.9001 75.48 517.51 Tm (u )Tj /T1_0 1 Tf 0.05 Tc 8.5774 0 0 8.3 106.83 517.69 Tm (and )Tj 8.5495 0 0 8.3 123.28 517.69 Tm (take )Tj /T1_2 1 Tf 0 Tc 7.8001 0 0 7.8001 151.31 500.95 Tm (1 )Tj /T1_0 1 Tf 0.05 Tc 8.4231 0 0 8.4 164.24 500.95 Tm (\(i )Tj /T1_2 1 Tf 0 Tc 8 0 0 8 164.2 490.51 Tm [(\( )162(i )]TJ /T1_3 1 Tf 0.05 Tc 9.6107 0 0 8.5 201.81 500.95 Tm (,u )Tj /T1_1 1 Tf -0.035 Tc 8.0108 0 0 8.9 220.15 500.95 Tm (1\) )Tj /T1_3 1 Tf 9.1855 0 0 11.1 182.08 490.33 Tm (u\) )Tj 0 Tc 8.1 0 0 8.1 181.91 479.89 Tm (u )Tj 0.05 Tc 9.9341 0 0 8.1 197.46 479.89 Tm (1,u+2, )Tj 10.5133 0 0 8.1 228.68 479.89 Tm (... )Tj 9.2876 0 0 8.1 240.15 479.89 Tm (,2u )Tj 9.7637 0 0 8.1 263.71 479.89 Tm (1,2u+ )Tj 11.1843 0 0 8.1 300.85 480.25 Tm (... )Tj 11.5495 0 0 8.1 312.88 480.25 Tm (,3u-1\) )Tj 8.2787 0 0 8.1 181.9 469.45 Tm (3u, )Tj /T1_1 1 Tf -0.035 Tc 5.4623 0 0 7.6 194.86 469.45 Tm (311 )Tj 0 Tc 12.2 0 0 12.2 205.96 469.45 Tm (+ )Tj /C0_0 1 Tf 4.1401 0 0 6.6601 182.17 458.83 Tm <003B007E0075002B0020>Tj /T1_3 1 Tf 0.05 Tc 9.6912 0 0 8.1 209.43 458.83 Tm (3u+3, )Tj 9.6295 0 0 8.1 241.29 458.83 Tm (.. )Tj 9.2876 0 0 8.1 248.97 458.83 Tm (,4u )Tj 8.3572 0 0 8.1 272.37 458.83 Tm (1\) )Tj /T1_0 1 Tf 8.8085 0 0 8.3 58.61 439.75 Tm (Then )Tj -0.029 Tc 8.2 0 0 8.2 149.7 416.17 Tm (I} )Tj -0.0098 Tc 8 0 0 8 224.77 397.45 Tm (I} )Tj /C0_0 1 Tf 0 Tc 3.9601 0 0 5.7601 117.91 378.55 Tm <003A007E0075002B0020>Tj /T1_2 1 Tf 10.2 0 0 10.2 116.29 368.65 Tm (+ )Tj -0.035 Tc 7.0951 0 0 7.3001 124.33 368.65 Tm (1, )Tj /T1_3 1 Tf 0.05 Tc 8.5357 0 0 7.9001 131.86 368.65 Tm (3u+ )Tj /T1_0 1 Tf 0.0056 Tc 8.2 0 0 8.2 215.21 369.37 Tm (l} )Tj 0.0412 Tc 8.3 0 0 8.3 58.85 349.93 Tm (which )Tj 0.0064 Tc 9 0 0 9 123.83 350.11 Tm ({i )Tj 0.05 Tc 8.3331 0 0 8.3 204.82 350.29 Tm (the )Tj 0.0327 Tc 8.3 0 0 8.3 219.06 350.29 Tm (union )Tj 0.05 Tc 8.3469 0 0 8.3 242.56 350.29 Tm (of )Tj 0.0308 Tc 8.2 0 0 8.2 63.39 318.97 Tm ({i )Tj 0 Tc 1.083 0 Td (-)Tj /T1_3 1 Tf -0.035 Tc 7.7044 0 0 7.9001 123.27 319.15 Tm (2, )Tj 0.05 Tc 9.6185 0 0 7.9001 131.31 319.15 Tm (... )Tj 8.9075 0 0 7.9001 141.87 319.15 Tm (,u )Tj /T1_2 1 Tf 0 Tc 7.1 0 0 7.1 63.67 309.61 Tm [({ )67(i )]TJ 0.025 -1.318 Td [({ )92(i )]TJ 10.2 0 0 10.2 122.05 298.27 Tm (+ )Tj 0.05 Tc 13.2414 0 0 7.1 130.61 298.27 Tm (l''''j )Tj 0 Tc 10.2 0 0 10.2 187.57 300.25 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.5513 0 0 7.7 195.58 300.25 Tm (1, )Tj 0.05 Tc 9.3635 0 0 7.7 203.03 300.25 Tm (... )Tj /T1_3 1 Tf 8.0583 0 0 7.9001 213.33 300.25 Tm (,3u )Tj /T1_0 1 Tf 0.0127 Tc 8 0 0 8 234.49 300.43 Tm (I} )Tj 0.0088 Tc 8.2 0 0 8.2 63.57 281.71 Tm ({i )Tj -0.0274 Tc 1.061 0 Td (--)Tj /T1_2 1 Tf 0 Tc 14.4 0 0 14.4 100.58 280.63 Tm (I )Tj /T1_3 1 Tf 0.05 Tc 9.0446 0 0 7.9001 109.9 280.63 Tm (=3u,3u+2,3u+ )Tj 8.1949 0 0 7.9001 190.11 281.89 Tm (,4u )Tj /T1_0 1 Tf 0 Tc 7.9001 0 0 7.9001 203.49 281.89 Tm (-)Tj -0.035 Tc 7.3939 0 0 7.4001 210.74 281.89 Tm (2} )Tj /T1_2 1 Tf 0 Tc 7.1 0 0 7.1 63.85 272.53 Tm [({ )92(i )]TJ /T1_1 1 Tf 7.3001 0 0 7.3001 104.88 272.35 Tm (i )Tj /T1_3 1 Tf 0.05 Tc 7.9091 0 0 7.9001 109.93 272.35 Tm (=3u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 126.19 272.35 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.2717 0 0 7.5001 134.39 272.35 Tm (1, )Tj 0.0143 Tc 7.5001 0 0 7.5001 141.47 272.35 Tm (:iu )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 151.57 272.35 Tm (+ )Tj -0.0006 Tc 1.561 0 Td (... )Tj 0 Tc 1.026 0 Td (, )Tj /T1_0 1 Tf 7.7 0 0 7.7 191.61 272.71 Tm (-)Tj 0.05 Tc 7.9223 0 0 7.7 199.17 272.71 Tm (3,4u )Tj -0.035 Tc 8.0284 0 0 8.2 224.77 272.53 Tm (I} )Tj 0.0412 Tc 8.3 0 0 8.3 59.03 253.81 Tm (which )Tj /T1_3 1 Tf 0.0424 Tc 8.5 0 0 8.5 116.81 253.45 Tm (St. )Tj /T1_2 1 Tf 0 Tc 7.8001 0 0 7.8001 74.45 237.07 Tm (1 )Tj /T1_0 1 Tf 0.0384 Tc 8.2 0 0 8.2 104.91 237.43 Tm (4\) )Tj 0.05 Tc 9.3958 0 0 8.3 59.18 223.57 Tm (Put )Tj /T1_3 1 Tf 0 Tc 8.5 0 0 8.5 76.61 223.57 Tm (u )Tj /T1_2 1 Tf -0.0139 Tc 8 0 0 8 116.2 223.57 Tm (1\) )Tj /T1_0 1 Tf 0.05 Tc 8.45 0 0 8.3 143.44 223.75 Tm (take )Tj /T1_2 1 Tf -0.035 Tc 16.4826 0 0 34.5 116.14 199.09 Tm (rU )Tj 0 Tc 34.5 0 0 34.5 135.58 199.09 Tm (-)Tj 8.3 0 0 8.3 144.02 199.09 Tm (i )Tj 12.5 0 0 12.5 149.02 199.09 Tm (+ )Tj 7.8001 0 0 7.8001 158.01 199.09 Tm (I )Tj /T1_1 1 Tf 1.664 0.992 Td [(\( )179(i )]TJ /T1_0 1 Tf -0.028 Tc 8.3 0 0 8.3 188.53 207.01 Tm (1, )Tj 0.05 Tc 10.7011 0 0 8.3 196.7 207.01 Tm (... )Tj 0 Tc 8.3 0 0 8.3 207.95 207.01 Tm [(, )51(u )]TJ -0.0242 Tc 2.301 -0.022 Td (1\) )Tj /T1_3 1 Tf 0.05 Tc 13.067 0 0 8.1 124.27 196.75 Tm (u-1 )Tj /T1_1 1 Tf 0.0462 Tc 8.7 0 0 8.7 170.96 196.39 Tm (\(i )Tj /T1_3 1 Tf -0.035 Tc 5.6427 0 0 8.1 188.36 196.57 Tm (1L\) )Tj /T1_0 1 Tf 0.017 Tc 5.9001 0 0 5.9001 85.44 185.77 Tm (7r2 )Tj 0 Tc 1.585 0 Td (\( )Tj 0.0198 Tc 8.8 0 0 8.8 98.21 185.77 Tm (i\) )Tj /T1_3 1 Tf 0.05 Tc 8.5088 0 0 8.1 124.13 185.95 Tm (4u )Tj /T1_2 1 Tf 0 Tc 8 0 0 8 144.03 185.95 Tm (i )Tj 12.4 0 0 12.4 149.02 185.95 Tm (+ )Tj /T1_0 1 Tf 7.4001 0 0 7.4001 157.82 185.95 Tm (2 )Tj /T1_1 1 Tf 7.7 0 0 7.7 170.99 186.31 Tm [(\( )150(i )]TJ /T1_3 1 Tf 0.05 Tc 10.5836 0 0 8.1 188.55 186.13 Tm (u+1,u+2, )Tj 10.9607 0 0 8.1 235.15 186.13 Tm (... )Tj 0 Tc 8.1 0 0 8.1 246.81 186.13 Tm (, )Tj -0.035 Tc 6.1118 0 0 8.1 124.15 175.87 Tm (41L )Tj /T1_0 1 Tf 0 Tc 8.1 0 0 8.1 135.99 175.87 Tm (-)Tj /T1_3 1 Tf 0.05 Tc 16.4907 0 0 8.1 144.15 175.87 Tm (i-I )Tj /T1_1 1 Tf 8.9435 0 0 8.9 170.96 175.51 Tm (\(i )Tj /T1_2 1 Tf -0.035 Tc 4.5927 0 0 8.1 179.75 175.51 Tm (== )Tj /T1_0 1 Tf 0.05 Tc 8.5283 0 0 8.3 188.36 175.51 Tm (3u )Tj /T1_2 1 Tf 0 Tc 12.5 0 0 12.5 199.78 175.51 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 8.2747 0 0 8.3 208.03 175.51 Tm (2, )Tj 0.05 Tc 8.3507 0 0 8.3 216.08 175.51 Tm (3u )Tj /T1_2 1 Tf 0 Tc 12.4 0 0 12.4 227.14 175.51 Tm (+ )Tj /T1_0 1 Tf 0.0026 Tc 8.3 0 0 8.3 235.23 175.51 Tm (4, )Tj 0.05 Tc 9.5784 0 0 8.3 243.7 175.51 Tm (.. )Tj /T1_3 1 Tf 8.6824 0 0 8.1 123.94 165.25 Tm (4u )Tj /T1_0 1 Tf -0.0198 Tc 8.1 0 0 8.1 135.81 165.25 Tm (--)Tj /T1_2 1 Tf 0 Tc 8 0 0 8 144.03 165.25 Tm (i )Tj 12.5 0 0 12.5 149.02 165.25 Tm (+ )Tj /T1_0 1 Tf 8.3 0 0 8.3 157.58 165.25 Tm (3 )Tj 0.05 Tc 8.4231 0 0 8.4 170.9 165.07 Tm (\(i )Tj /T1_2 1 Tf -0.035 Tc 4.7567 0 0 8.1 179.39 165.07 Tm (== )Tj /T1_0 1 Tf 0.05 Tc 8.5283 0 0 8.3 188.18 165.07 Tm (3u )Tj /T1_2 1 Tf 0 Tc 12.5 0 0 12.5 199.6 165.07 Tm (+ )Tj /T1_0 1 Tf 0.0026 Tc 8.3 0 0 8.3 207.8 165.07 Tm (3, )Tj /T1_3 1 Tf 0.05 Tc 8.2432 0 0 8.1 215.92 165.07 Tm (3u )Tj /T1_2 1 Tf 0 Tc 12.5 0 0 12.5 226.96 165.07 Tm (+ )Tj /T1_0 1 Tf 0.0215 Tc 8.3 0 0 8.3 235.15 165.07 Tm (5, )Tj 0.05 Tc 9.5784 0 0 8.3 243.7 165.07 Tm (.. )Tj 8.8908 0 0 8.3 58.96 145.99 Tm (Then )Tj -0.0209 Tc 8.3 0 0 8.3 109.01 146.35 Tm (is )Tj 0.05 Tc 8.8795 0 0 8.3 117.7 146.35 Tm (the )Tj 0.0436 Tc 8.3 0 0 8.3 133.02 146.35 Tm (union )Tj 0.05 Tc 8.5556 0 0 8.3 156.88 146.35 Tm (of )Tj 0.0025 Tc 8.3 0 0 8.3 181.53 146.35 Tm (following )Tj 0.0296 Tc 4.355 0 Td (sets )Tj /T1_2 1 Tf 0 Tc 14.6 0 0 14.6 89.78 100.45 Tm (I )Tj /T1_3 1 Tf -0.0205 Tc 7.9001 0 0 7.9001 95.12 122.23 Tm (i==1,2, )Tj 0.05 Tc 10.0659 0 0 7.9001 121.22 122.23 Tm (... )Tj 11.3029 0 0 7.9001 131.98 122.23 Tm (,u-1} )Tj /C0_0 1 Tf 0 Tc 2.3401 0 0 14.9401 95.05 103.14 Tm <007E0020>Tj /T1_3 1 Tf 0.05 Tc 9.6902 0 0 7.9001 112.06 103.14 Tm (+1,u+2, )Tj 9.8422 0 0 7.9001 149.67 103.14 Tm (... )Tj 8.9332 0 0 7.9001 160.41 103.14 Tm (,2u,2u+2, )Tj 9.3949 0 0 7.9001 201.15 103.14 Tm (... )Tj 9.7733 0 0 7.9001 211.54 103.14 Tm (,3u+l} )Tj /C0_0 1 Tf 0 Tc 2.8543 0 0 8.1 66.6 83.35 Tm <007B0037007200320028007E00290020>Tj /T1_2 1 Tf 14.2 0 0 14.2 90.33 83.35 Tm (I )Tj /C0_0 1 Tf 1.98 0 0 8.1 95.41 83.35 Tm <007E0020>Tj /T1_0 1 Tf 0.05 Tc 10.4498 0 0 7.7 99.82 83.35 Tm (:3u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 116.11 83.35 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.499 0 0 7.7 124.34 83.35 Tm (2, )Tj /T1_3 1 Tf -0.0193 Tc 7.9001 0 0 7.9001 131.87 83.35 Tm (3u )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 141.85 83.35 Tm (+ )Tj /T1_0 1 Tf -0.0334 Tc 7.7 0 0 7.7 149.73 83.35 Tm (4, )Tj 0.05 Tc 9.8094 0 0 7.7 157.84 83.35 Tm (... )Tj 0 Tc 7.7 0 0 7.7 168.36 83.35 Tm (, )Tj /T1_3 1 Tf 0.0363 Tc 7.9001 0 0 7.9001 171.29 83.35 Tm (4u} )Tj /T1_0 1 Tf -0.035 Tc 7.0962 0 0 8.3 66.13 75.06 Tm ({7r2\(Z\) )Tj /T1_3 1 Tf 0.05 Tc 9.7784 0 0 7.9001 95.31 75.06 Tm (z-3u+3,3u+5, )Tj 9.6185 0 0 7.9001 157.95 75.06 Tm (... )Tj 9.9011 0 0 7.9001 168.52 75.06 Tm (,4u+l} )Tj /T1_0 1 Tf 0 Tc 7.8001 0 0 7.8001 204.88 41.05 Tm (8 )Tj /T1_2 1 Tf 10.2 0 0 10.2 335.17 396.91 Tm (+ )Tj /T1_0 1 Tf -0.035 Tc 7.5513 0 0 7.7 343.18 396.91 Tm (1, )Tj 8.0066 0 0 8.2 342.45 379.09 Tm (--)Tj -0.0071 Tc 8.2 0 0 8.2 350.4 379.09 Tm (I} )Tj 0 Tc 8.3 0 0 8.3 334.52 319.15 Tm (-)Tj -0.035 Tc 8.2646 0 0 8.3 342.66 319.15 Tm (I} )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 304.75 300.25 Tm (+ )Tj -0.035 Tc 9.2774 0 0 10.2 328.07 300.25 Tm (., )Tj /T1_3 1 Tf 0.0159 Tc 7.9001 0 0 7.9001 334.73 300.25 Tm (4u )Tj /T1_0 1 Tf 0 Tc 1.342 0 Td (-)Tj -0.035 Tc 7.499 0 0 7.8001 352.94 300.25 Tm (2, )Tj 7.783 0 0 8.2 304.51 291.07 Tm (2} )Tj 7.698 0 0 7.7 286.65 281.71 Tm (3, )Tj /T1_2 1 Tf 0 Tc 10.2 0 0 10.2 304.75 281.71 Tm (+ )Tj 0.0082 Tc 1.561 0 Td (... )Tj 0 Tc 1.061 0 Td (, )Tj /T1_0 1 Tf 0.0205 Tc 7.7 0 0 7.7 334.77 281.71 Tm (4u )Tj 0 Tc 1.371 0 Td 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8.4026 0 0 8.4 89.02 405.91 Tm (component )Tj 0.0374 Tc 8.4 0 0 8.4 132.93 405.91 Tm (equal )Tj 0.05 Tc 8.5127 0 0 8.4 155.5 405.91 Tm (to )Tj 0.0071 Tc 8.4 0 0 8.4 166.03 405.91 Tm (1, )Tj 0.05 Tc 8.6949 0 0 8.4 175.59 405.91 Tm (and )Tj -0.0066 Tc 8.4 0 0 8.4 192.3 405.91 Tm (so )Tj 0.0324 Tc 1.277 0 Td (has )Tj 0.0142 Tc 1.8 0 Td (weight )Tj 0.05 Tc 8.6095 0 0 8.4 31.43 395.47 Tm (Thus )Tj -0.035 Tc 8.4184 0 0 14.1 54.1 395.47 Tm (G\) )Tj -0.007 Tc 8.4 0 0 8.4 66.35 395.47 Tm (is )Tj 0.0067 Tc 1.048 0 Td (even, )Tj 0.013 Tc 2.552 0 Td (i.e. )Tj /T1_4 1 Tf 0 Tc 8.1 0 0 8.1 111.91 395.47 Tm (v )Tj /T1_3 1 Tf 8.4 0 0 8.4 127.71 395.47 Tm (0 )Tj 0.05 Tc 8.5556 0 0 8.4 134.74 395.47 Tm (or )Tj 0 Tc 8.4 0 0 8.4 145.87 395.47 Tm (1 )Tj 0.0458 Tc 0.815 0 Td (\(mod )Tj 0.034 Tc 2.644 0 Td (4\). )Tj /T1_6 1 Tf 0 Tc 8.7 0 0 8.7 335.08 396.0099 Tm (o )Tj /T1_3 1 Tf 0.05 Tc 8.6891 0 0 8.4 31.61 376.39 Tm (The )Tj 0.0409 Tc 8.4 0 0 8.4 49.67 376.39 Tm (rest )Tj 0.05 Tc 8.5556 0 0 8.4 66.34 376.39 Tm (of )Tj 0.0447 Tc 8.4 0 0 8.4 76.66 376.39 Tm (the )Tj 0.05 Tc 8.7387 0 0 8.4 90.91 376.39 Tm (paper )Tj 0.0121 Tc 8.4 0 0 8.4 115.13 376.39 Tm (gives )Tj 0.0434 Tc 2.57 0 Td (constructions )Tj 0.0181 Tc 6.256 0 Td (for )Tj /T1_4 1 Tf 0.05 Tc 9.2978 0 0 8.1 203.03 376.39 Tm (GBRDs )Tj /T1_3 1 Tf 0.0309 Tc 8.4 0 0 8.4 236.87 376.39 Tm (with )Tj /T1_4 1 Tf 0 Tc 8.1 0 0 8.1 256.48 376.39 Tm (k )Tj /T1_6 1 Tf 8 0 0 8 264.11 376.39 Tm (= )Tj /T1_3 1 Tf 8.4 0 0 8.4 274.22 376.39 Tm (3 )Tj 0.05 Tc 8.4599 0 0 8.4 281.43 376.39 Tm (and )Tj 0.0381 Tc 8.4 0 0 8.4 298.25 376.39 Tm (with )Tj /T1_4 1 Tf 0 Tc 2.313 0 Td (k )Tj /T1_3 1 Tf 12.1 0 0 12.1 325.38 376.39 Tm (= )Tj 0.0153 Tc 8.4 0 0 8.4 334.41 376.39 Tm (4. )Tj /T1_4 1 Tf 0.05 Tc 8.3821 0 0 8.1 18.35 365.77 Tm (St )Tj /T1_3 1 Tf -0.009 Tc 8.4 0 0 8.4 29.69 365.77 Tm (will )Tj 0.0435 Tc 2.027 0 Td (denote )Tj 0.05 Tc 8.4697 0 0 8.4 74.86 365.77 Tm (the )Tj 0.0455 Tc 8.4 0 0 8.4 89.52 365.77 Tm (subset )Tj /T1_4 1 Tf 0.05 Tc 8.7394 0 0 8.1 117 365.77 Tm ({1,2, )Tj 10.737 0 0 8.1 137.96 365.77 Tm (... )Tj 10.5709 0 0 8.1 149.26 365.77 Tm (,t )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 158.31 365.77 Tm (-)Tj /T1_4 1 Tf 0.05 Tc 11.2005 0 0 8.1 167.28 365.77 Tm (l,t )Tj /T1_6 1 Tf 0 Tc 12.2 0 0 12.2 180.52 365.77 Tm (+ )Tj /T1_4 1 Tf 0.0041 Tc 8.1 0 0 8.1 189.94 365.77 Tm (1, )Tj 0.05 Tc 10.9607 0 0 8.1 198.07 365.77 Tm (... )Tj 9.3708 0 0 8.1 209.55 365.77 Tm (,2t )Tj /T1_6 1 Tf 15.8096 0 0 8.9 222.87 365.77 Tm (-I} )Tj /T1_3 1 Tf 0.0231 Tc 8.4 0 0 8.4 243.1 365.77 Tm (of )Tj /T1_4 1 Tf 0.0027 Tc 8.1 0 0 8.1 253.81 365.77 Tm (Z2t )Tj /T1_3 1 Tf 0.05 Tc 8.4657 0 0 8.4 268.91 365.77 Tm (where )Tj /T1_4 1 Tf 12.574 0 0 8.1 294.69 365.77 Tm (tEN. )Tj /T1_3 1 Tf 0.0392 Tc 8.4 0 0 8.4 326.06 365.77 Tm (\(We )Tj 0.044 Tc -36.662 -1.221 Td (assume )Tj 0.05 Tc 9.084 0 0 8.4 48.22 355.5099 Tm (that )Tj -0.035 Tc 8.316 0 0 8.4 66.59 355.5099 Tm (we )Tj 0.0447 Tc 8.4 0 0 8.4 79.12 355.5099 Tm (add )Tj 0.05 Tc 8.6949 0 0 8.4 95.31 355.5099 Tm (and )Tj 0.0405 Tc 8.4 0 0 8.4 112.12 355.5099 Tm (multiply )Tj 0.0315 Tc 4.106 0 Td (elements )Tj 0.05 Tc 8.7642 0 0 8.4 181.18 355.5099 Tm (of )Tj /T1_4 1 Tf 8.3821 0 0 8.1 191.69 355.5099 Tm (St )Tj /T1_3 1 Tf -0.0067 Tc 8.4 0 0 8.4 202.6 355.5099 Tm (as )Tj 0.0285 Tc 1.22 0 Td (elements )Tj 0.05 Tc 8.5556 0 0 8.4 247.42 355.5099 Tm (of )Tj /T1_4 1 Tf 0.0222 Tc 8.1 0 0 8.1 257.59 355.5099 Tm (Z2t. )Tj /T1_3 1 Tf 0.05 Tc 8.7991 0 0 8.4 31.61 344.89 Tm (The )Tj 0.007 Tc 8.4 0 0 8.4 49.23 344.89 Tm (fonowing )Tj 0.05 Tc 8.4984 0 0 8.4 84.89 344.89 Tm (lemma )Tj -0.035 Tc 8.1972 0 0 8.4 112.61 344.89 Tm (is )Tj 0.0334 Tc 8.4 0 0 8.4 128.45 344.89 Tm (generalisation )Tj 0.05 Tc 8.7642 0 0 8.4 182.8 344.89 Tm (of )Tj 8.4504 0 0 8.4 192.73 344.89 Tm (Lemma )Tj -0.0065 Tc 8.4 0 0 8.4 223.46 344.89 Tm (3.1 )Tj -0.035 Tc 7.5699 0 0 8.4 237.42 344.89 Tm ([4J. )Tj 0.05 Tc 9.9514 0 0 8.1 18.13 326.17 Tm (Lemma )Tj 8.6546 0 0 8.1 53.77 326.17 Tm (2.3 )Tj /T1_4 1 Tf 9.6309 0 0 8.1 70.66 326.17 Tm (If )Tj 0.0163 Tc 8.1 0 0 8.1 79.65 326.17 Tm (there )Tj 0.05 Tc 8.1269 0 0 8.1 100.55 326.17 Tm (exist )Tj -0.0079 Tc 9.2 0 0 9.2 26.46 309.25 Tm (\(i\) )Tj 0 Tc 8.1 0 0 8.1 40.12 309.25 Tm (k )Tj /T1_3 1 Tf 1.147 0 Td (-)Tj /T1_6 1 Tf 8 0 0 8 60.22 309.25 Tm (1 )Tj /T1_4 1 Tf 0.05 Tc 8.2167 0 0 8.1 70.84 309.25 Tm (permutations )Tj /T1_3 1 Tf -0.035 Tc 6.183 0 0 6.2 125.4 309.25 Tm (7I"I, )Tj 5.147 0 0 6.2 137.83 309.25 Tm (71"2, )Tj 0.05 Tc 10.7011 0 0 6.2 150.26 309.25 Tm (... )Tj 0 Tc 6.2 0 0 6.2 161.55 309.25 Tm (, )Tj 0.05 Tc 6.2879 0 0 6.2 165.18 309.25 Tm (7I"k-l )Tj /T1_4 1 Tf 9.3692 0 0 8.1 189.64 309.25 Tm (of )Tj 8.3869 0 0 8.1 203.03 309.25 Tm (St, )Tj 17.9364 0 0 8.1 220.82 309.25 Tm (tEN, )Tj 8.4668 0 0 8.1 264.45 309.25 Tm (such )Tj 0.047 Tc 8.1 0 0 8.1 288.45 309.25 Tm (that )Tj 0.05 Tc 8.1079 0 0 8.1 308.23 309.25 Tm (for )Tj 0.033 Tc 8.1 0 0 8.1 325.93 309.25 Tm (all )Tj /T1_5 1 Tf 0.05 Tc 10.0526 0 0 8 39.48 298.45 Tm (P,qE{I, )Tj 10.1817 0 0 8 75.07 298.45 Tm (... )Tj 8.8961 0 0 8 86.52 298.45 Tm (,k )Tj /T1_3 1 Tf 0.0046 Tc 9.2 0 0 9.2 105.42 298.45 Tm (I}, )Tj /T1_5 1 Tf -0.0254 Tc 8 0 0 8 121.89 298.45 Tm (p:::j:.q, )Tj /T1_4 1 Tf 0.05 Tc 8.2056 0 0 8.1 23.78 259.03 Tm (\(ii\) )Tj /T1_5 1 Tf 0 Tc 7.1 0 0 7.1 40.23 259.03 Tm (a )Tj /T1_4 1 Tf 0.05 Tc 9.2799 0 0 8.1 47.33 259.03 Tm (GBRD\(v,k,2;Z2\) )Tj 0 Tc 8.1 0 0 8.1 120.58 259.03 Tm (\225 )Tj 0.05 Tc 8.1101 0 0 8.1 21.08 241.9299 Tm (\(iii\) )Tj 0 Tc 7.7 0 0 7.7 40.27 241.9299 Tm (a )Tj 0.05 Tc 10.3505 0 0 8.1 47.6 241.9299 Tm (BIBD\(v,k,I\). )Tj 8.4019 0 0 8.1 18.26 225.3699 Tm (then )Tj 0.0219 Tc 8.1 0 0 8.1 38.07 225.3699 Tm (there )Tj 0.05 Tc 8.14 0 0 8.1 58.97 225.3699 Tm (exists )Tj 0 Tc 8.4 0 0 8.4 82.39 225.3699 Tm (a )Tj 0.05 Tc 9.2978 0 0 8.1 88.91 225.3699 Tm (GBRD\(v,k,2t;Z2t\). )Tj /T1_3 1 Tf 0.0337 Tc 8.3 0 0 8.3 330.56 280.09 Tm (\(2\) )Tj 0.05 Tc 9.5477 0 0 8.4 17.96 197.6499 Tm (Proof: )Tj 0.0174 Tc 8.4 0 0 8.4 50.34 197.6499 Tm (In )Tj 0.05 Tc 8.6063 0 0 8.4 61.54 197.6499 Tm (the )Tj 0.0269 Tc 8.4 0 0 8.4 148.49 197.6499 Tm (replace )Tj 0.0326 Tc 3.505 0 Td (each )Tj 0 Tc 2.44 0 Td (1 )Tj -0.0047 Tc 0.871 0 Td (by )Tj /T1_4 1 Tf -0.0122 Tc 9.2 0 0 9.2 218.05 197.6499 Tm (t, )Tj /T1_3 1 Tf 0.05 Tc 8.731 0 0 8.4 226.96 197.6499 Tm (to )Tj -0.0184 Tc 8.4 0 0 8.4 237.89 197.6499 Tm (give )Tj 0 Tc 2.142 0 Td (a )Tj 0.05 Tc 8.8973 0 0 8.4 263.5 197.6499 Tm (matrix )Tj /T1_4 1 Tf 0.0344 Tc 8.7 0 0 8.7 292.63 197.6499 Tm (A. )Tj /T1_3 1 Tf 0.0054 Tc 8.4 0 0 8.4 306.31 197.6499 Tm (Let )Tj /T1_4 1 Tf 0 Tc 8.7 0 0 8.7 321.9 197.6499 Tm (B )Tj /T1_3 1 Tf 0.05 Tc 8.6029 0 0 8.4 332.11 197.6499 Tm (be )Tj 8.7429 0 0 8.4 17.8 187.21 Tm (the )Tj 0.0193 Tc 8.4 0 0 8.4 32.51 187.21 Tm (incidence )Tj 0.05 Tc 8.5187 0 0 8.4 69.46 187.21 Tm (matrix )Tj 8.5556 0 0 8.4 96.58 187.21 Tm (of )Tj 8.6063 0 0 8.4 106.36 187.21 Tm (the )Tj /T1_5 1 Tf -0.0243 Tc 8.3 0 0 8.3 158.32 187.21 Tm (k, )Tj /T1_3 1 Tf 0.0406 Tc 8.4 0 0 8.4 166.93 187.21 Tm (1\), )Tj 0.05 Tc 8.5244 0 0 8.4 179.45 187.21 Tm (with )Tj 0.0382 Tc 8.4 0 0 8.4 198.81 187.21 Tm (entries )Tj 0 Tc 3.29 0 Td (* )Tj 0.0447 Tc 0.825 0 Td (and )Tj -0.035 Tc 6.4936 0 0 8.4 249.42 187.21 Tm (O. )Tj 0.05 Tc 8.613 0 0 8.4 259.88 187.21 Tm (Form )Tj 0 Tc 8.4 0 0 8.4 282.88 187.21 Tm (a )Tj -0.0273 Tc 0.823 0 Td (new )Tj 0.0247 Tc 1.964 0 Td (incidence )Tj 0.05 Tc 8.8342 0 0 8.4 17.62 176.95 Tm (matrix )Tj 0 Tc 13.2 0 0 13.2 45.94 176.95 Tm (e )Tj 0.0174 Tc 8.4 0 0 8.4 55.35 176.95 Tm (from )Tj /T1_4 1 Tf 0 Tc 8.7 0 0 8.7 76.02 176.95 Tm (B )Tj /T1_3 1 Tf -0.0309 Tc 8.4 0 0 8.4 85.51 176.95 Tm (by, )Tj 0.0311 Tc 1.583 0 Td (replacing )Tj 0.032 Tc 4.343 0 Td (in )Tj 0.0183 Tc 1.219 0 Td (each )Tj 0.0389 Tc 2.273 0 Td (column )Tj 0.05 Tc 8.7642 0 0 8.4 195.04 176.95 Tm (of )Tj /T1_4 1 Tf 9.4882 0 0 8.7 205.09 176.95 Tm (B, )Tj /T1_3 1 Tf 0.0308 Tc 8.4 0 0 8.4 26 160.21 Tm (\(i\) )Tj 0.0183 Tc 1.608 0 Td (each )Tj 0 Tc 2.283 0 Td (* )Tj 0.0167 Tc 0.857 0 Td (by )Tj 0 Tc 1.404 0 Td (a )Tj -0.0166 Tc 0.844 0 Td (row )Tj /T1_4 1 Tf 0.05 Tc 9.6206 0 0 8.1 101.08 160.21 Tm (of2t )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 120.51 160.21 Tm (-)Tj 8.4 0 0 8.4 128.83 160.21 Tm (2 )Tj 0.05 Tc 10.3478 0 0 8.4 136.05 160.21 Tm (*'s. )Tj 0.0139 Tc 8.4 0 0 8.4 23.66 142.9299 Tm (\(ii\) )Tj 0.05 Tc 9.7794 0 0 8.4 39.58 142.9299 Tm (the;th )Tj 0 Tc 8.4 0 0 8.4 67.77 142.9299 Tm (0 )Tj 0.0167 Tc 0.826 0 Td (by )Tj 0.05 Tc 6.8103 0 0 6.2 86.51 142.9299 Tm (7I"j\(I\), )Tj 7.7249 0 0 6.2 109.86 142.9299 Tm (\225\225\225 )Tj 0 Tc 6.2 0 0 6.2 121.23 142.9299 Tm (, )Tj /T1_4 1 Tf -0.035 Tc 7.7186 0 0 8.1 124.84 142.9299 Tm (7I"j\(2t )Tj /T1_3 1 Tf 0 Tc 8.1 0 0 8.1 146.25 142.9299 Tm (-)Tj -0.0116 Tc 8.4 0 0 8.4 154.51 142.9299 Tm (1\) )Tj 0.0154 Tc 8.3 0 0 8.3 21.14 126.19 Tm (\(iii\) )Tj 0.05 Tc 8.6063 0 0 8.4 39.58 126.19 Tm (the )Tj /T1_4 1 Tf 7.9839 0 0 6.4001 54.16 126.19 Tm (kth )Tj /T1_3 1 Tf 0 Tc 8.4 0 0 8.4 68.49 126.19 Tm (0 )Tj 0.0167 Tc 0.848 0 Td (by )Tj 0 Tc 1.382 0 Td (a )Tj 0.0048 Tc 0.823 0 Td (row )Tj 0.05 Tc 8.5556 0 0 8.4 110.44 126.19 Tm (of )Tj /T1_4 1 Tf 8.4144 0 0 8.1 120.57 126.19 Tm (2t )Tj /T1_3 1 Tf 10.8895 0 0 8.4 138.53 126.19 Tm (20's. )Tj /T1_6 1 Tf 11.5646 0 0 8.9 179.07 142.39 Tm (\(j )Tj /T1_3 1 Tf 0 Tc 12.1 0 0 12.1 189.3 142.39 Tm (= )Tj -0.035 Tc 8.6701 0 0 8.8 198.42 142.39 Tm (1, )Tj 0.05 Tc 10.7011 0 0 8.8 206.6 142.39 Tm (... )Tj /T1_5 1 Tf 9.1242 0 0 8.6 218.28 142.39 Tm (,k )Tj /T1_6 1 Tf 0 Tc 8.6 0 0 8.6 228.52 142.39 Tm (-)Tj /T1_3 1 Tf -0.035 Tc 8.6706 0 0 8.8 236.76 142.39 Tm (1\) )Tj 0 Tc 8.8 0 0 8.8 247.36 142.39 Tm (\225 )Tj 0.05 Tc 8.6438 0 0 8.4 31.25 108.72 Tm (Then )Tj /T1_4 1 Tf 10.1388 0 0 8.1 54.07 108.72 Tm (Bile )Tj /T1_3 1 Tf -0.0284 Tc 8.4 0 0 8.4 74.81 108.72 Tm (is )Tj 0 Tc 1.049 0 Td (a )Tj /T1_4 1 Tf 0.05 Tc 9.4617 0 0 8.1 90.17 108.72 Tm (GBRD\( )Tj 8.5581 0 0 8.5 121.45 108.72 Tm (v, )Tj 8.3645 0 0 8.1 129.94 108.72 Tm (k, )Tj 0.0076 Tc 8.1 0 0 8.1 138.21 108.72 Tm (2t; )Tj 0.0093 Tc 1.449 0 Td (Z2t\) )Tj /T1_3 1 Tf 0.0447 Tc 8.4 0 0 8.4 167.66 108.72 Tm (\(where )Tj /T1_6 1 Tf -0.035 Tc 6.9805 0 0 11.7 196.37 108.72 Tm (II )Tj /T1_3 1 Tf 0.0321 Tc 8.4 0 0 8.4 203.86 108.72 Tm (denotes )Tj 0.0473 Tc 3.664 0 Td (concatenation\). )Tj /T1_6 1 Tf 0 Tc 8.7 0 0 8.7 334.72 108.72 Tm (o )Tj /T1_3 1 Tf 0.05 Tc 9.8958 0 0 8.1 17.77 89.8199 Tm (Lemma )Tj 8.7898 0 0 8.1 53.41 89.8199 Tm (2.4 )Tj /T1_4 1 Tf 0.027 Tc 8.1 0 0 8.1 70.26 89.8199 Tm (For )Tj 0.033 Tc 1.964 0 Td (all )Tj /T1_5 1 Tf 0 Tc 7.3001 0 0 7.3001 97.98 89.8199 Tm (t )Tj /T1_3 1 Tf -0.035 Tc 5.2223 0 0 9.9 104.19 89.8199 Tm (2:: )Tj 0 Tc 8.1 0 0 8.1 113.01 89.8199 Tm (4 )Tj /T1_4 1 Tf 0.033 Tc 0.993 0 Td (there )Tj 0.05 Tc 8.1269 0 0 8.1 142.67 89.8199 Tm (exist )Tj 8.3601 0 0 8.1 162.31 89.8199 Tm (at )Tj 0.0295 Tc 8.1 0 0 8.1 172.89 89.8199 Tm (least )Tj 0.0371 Tc 2.467 0 Td (two )Tj 0.05 Tc 8.2475 0 0 8.1 208.72 89.8199 Tm (permutations )Tj /T1_3 1 Tf -0.035 Tc 5.2373 0 0 6.2 260.05 89.8199 Tm (71"1, )Tj 6.1047 0 0 6.2 273 89.8199 Tm (7r2 )Tj /T1_4 1 Tf 0.05 Tc 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)Tj 8.4239 0 0 8.3 278.55 569.17 Tm (element )Tj 8.3814 0 0 8.3 311.67 569.17 Tm (entries )Tj 8.3046 0 0 8.3 340.39 569.17 Tm (by )Tj -0.035 Tc 8.0526 0 0 8.3 353.06 569.17 Tm (1; )Tj 0.05 Tc 8.5777 0 0 8.3 31.84 558.18 Tm (then )Tj 0.0228 Tc 8.3 0 0 8.3 51.92 558.18 Tm (\(1\) )Tj /T1_2 1 Tf -0.0237 Tc 8.8 0 0 8.8 203.89 547.93 Tm (A\)1 )Tj /T1_3 1 Tf 0 Tc 12.2 0 0 12.2 218.14 547.93 Tm (+ )Tj /T1_2 1 Tf 0.05 Tc 8.8506 0 0 8.8 226.75 547.93 Tm (AJ )Tj /T1_0 1 Tf 9.084 0 0 8.3 31.84 532.99 Tm (that )Tj 0.0055 Tc 8.3 0 0 8.3 51.77 532.99 Tm (is, )Tj /T1_2 1 Tf 0 Tc 8.5 0 0 8.5 64.88 532.99 Tm (N )Tj /T1_0 1 Tf 0.0224 Tc 8.3 0 0 8.3 76.79 532.99 Tm (is )Tj 0.05 Tc 9.1527 0 0 8.3 87.64 532.99 Tm (the )Tj 0.0334 Tc 8.3 0 0 8.3 103.97 532.99 Tm (incidence )Tj 0.05 Tc 8.7711 0 0 8.3 143.08 532.99 Tm (matrix )Tj 8.3469 0 0 8.3 172.18 532.99 Tm (of )Tj 0 Tc 8.3 0 0 8.3 183.34 532.99 Tm (a )Tj /T1_2 1 Tf 8.5 0 0 8.5 192.12 532.99 Tm (B )Tj /T1_3 1 Tf 8 0 0 8 198.82 532.99 Tm (1 )Tj /T1_2 1 Tf 8.5 0 0 8.5 203.46 532.99 Tm (B )Tj 0.05 Tc 8.6053 0 0 8.5 210.14 532.99 Tm (D\( )Tj 0.0339 Tc 8.5 0 0 8.5 220.63 532.99 Tm (v, )Tj 0.038 Tc 0.999 0 Td (k, )Tj /T1_0 1 Tf 0.05 Tc 8.6095 0 0 8.3 256.25 532.99 Tm (Thus )Tj 0.0322 Tc 8.3 0 0 8.3 279.71 532.99 Tm (we )Tj 0.05 Tc 1.758 0 Td (use )Tj 9.1527 0 0 8.3 311.02 532.99 Tm (the )Tj 8.6503 0 0 8.3 327.59 532.99 Tm (notation )Tj /T1_2 1 Tf 8.7201 0 0 8.5 31.68 522.37 Tm (GBRD\('O,k, )Tj -0.035 Tc 7.5728 0 0 8.5 80.94 522.37 Tm (A; )Tj /T1_0 1 Tf 0.05 Tc 8.731 0 0 8.3 104.38 522.37 Tm (to )Tj 8.4298 0 0 8.3 115.84 522.37 Tm (denote )Tj 0 Tc 8.3 0 0 8.3 145 522.37 Tm (a )Tj 0.0303 Tc 0.999 0 Td (generalised )Tj 0.0471 Tc 5.425 0 Td (Bhaskar )Tj 0.05 Tc 8.5428 0 0 8.3 232.16 522.37 Tm (Rao )Tj 0.0308 Tc 8.3 0 0 8.3 251.2 522.37 Tm (design )Tj 0.05 Tc 8.7118 0 0 8.3 279.17 522.37 Tm (with )Tj 8.5118 0 0 8.3 300.34 522.37 Tm (one )Tj 0.0453 Tc 8.3 0 0 8.3 318.34 522.37 Tm (association )Tj 0.0169 Tc -34.504 -1.28 Td (class. )Tj 0.05 Tc 8.3459 0 0 8.3 55.66 511.75 Tm (Note )Tj 9.5218 0 0 8.3 75.76 511.75 Tm (that )Tj 0 Tc 8.3 0 0 8.3 94.6 511.75 Tm (a )Tj 0.0382 Tc 0.833 0 Td (necessary )Tj 0.0431 Tc 4.524 0 Td (condition )Tj 0.0038 Tc 4.445 0 Td (for )Tj 0.05 Tc 8.6063 0 0 8.3 188.62 511.75 Tm (the )Tj 0.0315 Tc 8.3 0 0 8.3 202.41 511.75 Tm (existence )Tj 0.05 Tc 8.7642 0 0 8.3 237.88 511.75 Tm (of )Tj 0 Tc 8.3 0 0 8.3 247.42 511.75 Tm (a )Tj /T1_2 1 Tf 0.05 Tc 9.745 0 0 8.5 253.96 511.75 Tm (GBRD\( )Tj 0.0339 Tc 8.5 0 0 8.5 286.15 511.75 Tm (v, )Tj 0.05 Tc 8.6035 0 0 8.5 294.64 511.75 Tm (k, )Tj -0.035 Tc 7.1743 0 0 8.5 303.77 511.75 Tm (A; )Tj /T1_3 1 Tf 9.1709 0 0 11.7 312.52 511.75 Tm (G\) )Tj /T1_0 1 Tf 0.0008 Tc 8.3 0 0 8.3 324.83 511.75 Tm (is )Tj /T1_3 1 Tf -0.035 Tc 10.1924 0 0 11.7 333.44 511.75 Tm (IGII )Tj /T1_2 1 Tf 7.9002 0 0 8.5 352.38 511.75 Tm (A. )Tj /T1_0 1 Tf 0.05 Tc 8.3459 0 0 8.3 45.4 501.13 Tm (Note )Tj 9.5218 0 0 8.3 67.3 501.13 Tm (that )Tj 9.1527 0 0 8.3 88 501.13 Tm (the )Tj 0.0423 Tc 8.3 0 0 8.3 104.31 501.13 Tm (existence )Tj 0.05 Tc 8.5556 0 0 8.3 142.48 501.13 Tm (of )Tj 0 Tc 8.3 0 0 8.3 153.82 501.13 Tm (a )Tj /T1_2 1 Tf 0.05 Tc 9.3349 0 0 8.5 161.99 501.13 Tm (GBRD\(v,k,A;G\) )Tj /T1_0 1 Tf 0.0146 Tc 8.3 0 0 8.3 231.75 501.13 Tm (for )Tj 0.0428 Tc 1.753 0 Td (some )Tj /T1_2 1 Tf 0.05 Tc 10.5439 0 0 8.5 269.22 501.13 Tm (v,k )Tj /T1_0 1 Tf 8.8124 0 0 8.3 287.19 501.13 Tm (and )Tj 0 Tc 8.3 0 0 8.3 305.92 501.13 Tm (G )Tj 0.0296 Tc 1.281 0 Td (implies )Tj 0.05 Tc 8.7429 0 0 8.3 347.38 501.13 Tm (the )Tj 0.0369 Tc 8.3 0 0 8.3 31.77 490.69 Tm (existence )Tj 0.05 Tc 8.9729 0 0 8.3 68.49 490.69 Tm (of )Tj 0 Tc 8.3 0 0 8.3 78.94 490.69 Tm (a )Tj /T1_1 1 Tf 0.037 Tc 7.9001 0 0 7.9001 126.46 490.69 Tm (k, )Tj -0.035 Tc 6.7629 0 0 8.2 135.18 490.69 Tm (CA; )Tj /T1_0 1 Tf 0.0038 Tc 8.3 0 0 8.3 160.65 490.69 Tm (for )Tj 0.0058 Tc 1.584 0 Td (all )Tj -0.0223 Tc 1.431 0 Td (c, )Tj -0.0145 Tc 1.095 0 Td (by )Tj 0.05 Tc 8.3755 0 0 8.3 206.2 490.69 Tm (concatenation. )Tj 8.4994 0 0 8.3 44.94 480.25 Tm (In )Tj 0.0475 Tc 8.3 0 0 8.3 57.22 480.25 Tm (this )Tj 0.05 Tc 9.1121 0 0 8.3 75.25 480.25 Tm (paper )Tj -0.035 Tc 8.1561 0 0 8.3 101.87 480.25 Tm (we )Tj 0.05 Tc 8.5325 0 0 8.3 115.65 480.25 Tm (are )Tj 0.0424 Tc 8.3 0 0 8.3 131.32 480.25 Tm (concerned )Tj 0.0289 Tc 4.966 0 Td (only )Tj 0.0312 Tc 2.394 0 Td (with )Tj 0.05 Tc 8.4697 0 0 8.3 212.92 480.25 Tm (the )Tj 0.034 Tc 8.3 0 0 8.3 228.52 480.25 Tm (case )Tj 0.0415 Tc 2.351 0 Td (where )Tj /T1_3 1 Tf 0 Tc 8.5 0 0 8.5 274.01 480.25 Tm (G )Tj /T1_0 1 Tf 0.0008 Tc 8.3 0 0 8.3 285.41 480.25 Tm (is )Tj 0.05 Tc 8.8795 0 0 8.3 295.72 480.25 Tm (the )Tj 8.5773 0 0 8.3 311.87 480.25 Tm (group )Tj /T1_2 1 Tf 8.1738 0 0 8.1 338.41 480.25 Tm (Zn )Tj /T1_0 1 Tf 8.5556 0 0 8.3 352.18 480.25 Tm (of )Tj 0.0463 Tc 8.3 0 0 8.3 31.43 469.81 Tm (integers )Tj 0.05 Tc 8.674 0 0 8.3 64.42 469.81 Tm (modulo )Tj /T1_2 1 Tf 0.0498 Tc 8.5 0 0 8.5 97.34 469.81 Tm (n. )Tj /T1_0 1 Tf -0.0131 Tc 8.3 0 0 8.3 110.49 469.81 Tm (We )Tj -0.0029 Tc 1.867 0 Td (will )Tj 0.0391 Tc 2.04 0 Td (use )Tj /T1_3 1 Tf 0 Tc 12.2 0 0 12.2 158.74 469.81 Tm (+ )Tj /T1_0 1 Tf 0.05 Tc 8.9493 0 0 8.3 168.46 469.81 Tm (to )Tj 8.3058 0 0 8.3 179.56 469.81 Tm (denote )Tj 8.6063 0 0 8.3 207.34 469.81 Tm (the )Tj 8.4198 0 0 8.3 222.39 469.81 Tm (addition )Tj 0.0199 Tc 8.3 0 0 8.3 257.15 469.81 Tm (in )Tj /T1_2 1 Tf 0.05 Tc 8.4944 0 0 8.1 268.03 469.81 Tm (Zn )Tj /T1_0 1 Tf 8.8713 0 0 8.3 282.14 469.81 Tm (\(the )Tj 8.4784 0 0 8.3 301.58 469.81 Tm ('multiplication' )Tj 8.5556 0 0 8.3 31.6 459.19 Tm (of )Tj 8.7429 0 0 8.3 41.74 459.19 Tm (the )Tj 8.5058 0 0 8.3 56.81 459.19 Tm (group )Tj 8.6949 0 0 8.3 129.51 459.19 Tm (and )Tj -0.035 Tc 4.5435 0 0 8.3 146.86 459.19 Tm (EB )Tj 0.05 Tc 8.731 0 0 8.3 156.4 459.19 Tm (to )Tj 8.6029 0 0 8.3 167.05 459.19 Tm (be )Tj 8.7429 0 0 8.3 178.72 459.19 Tm (the )Tj 0.042 Tc 8.3 0 0 8.3 193.96 459.19 Tm (addition )Tj 0.05 Tc 8.3469 0 0 8.3 227.26 459.19 Tm (of )Tj 8.7429 0 0 8.3 237.4 459.19 Tm (the )Tj 8.3628 0 0 8.3 252.47 459.19 Tm (group )Tj 0.0447 Tc 8.3 0 0 8.3 277.55 459.19 Tm (ring. )Tj 0.05 Tc 9.019 0 0 8.3 300.16 459.19 Tm (The )Tj 0.0306 Tc 8.3 0 0 8.3 318.92 459.19 Tm (zero )Tj 0.05 Tc 8.5556 0 0 8.3 337.24 459.19 Tm (of )Tj 8.7429 0 0 8.3 347.38 459.19 Tm (the )Tj 8.3628 0 0 8.3 31.61 448.93 Tm (group )Tj 0.049 Tc 8.3 0 0 8.3 56.33 448.93 Tm (ring )Tj 0.0188 Tc 2.19 0 Td (will )Tj 0.05 Tc 8.7859 0 0 8.3 91.63 448.93 Tm (be )Tj 8.4424 0 0 8.3 103.78 448.93 Tm (denoted )Tj 0.0289 Tc 8.3 0 0 8.3 136.27 448.93 Tm (by )Tj 0.05 Tc 7.3433 0 0 5.8001 148.71 448.93 Tm (*j )Tj 8.7429 0 0 8.3 158.02 448.93 Tm (the )Tj 8.349 0 0 8.3 172.55 448.93 Tm (identity )Tj 0.0332 Tc 8.3 0 0 8.3 204.04 448.93 Tm (of )Tj /T1_2 1 Tf 0.0158 Tc 8.1 0 0 8.1 214.21 448.93 Tm (Zn )Tj /T1_0 1 Tf 0.0072 Tc 8.3 0 0 8.3 226.99 448.93 Tm (by )Tj 0 Tc 1.42 0 Td (0 )Tj 0.0445 Tc 2.178 0 Td (usual. )Tj 0.0086 Tc -25.486 -1.258 Td (We )Tj 0.05 Tc 8.7684 0 0 8.3 59.84 438.49 Tm (further )Tj 8.5339 0 0 8.3 89.81 438.49 Tm (restrict )Tj 8.7151 0 0 8.3 119.97 438.49 Tm (attention )Tj 8.9493 0 0 8.3 156.94 438.49 Tm (to )Tj 8.6063 0 0 8.3 167.38 438.49 Tm (the )Tj 0.0268 Tc 8.3 0 0 8.3 181.72 438.49 Tm (case )Tj /T1_2 1 Tf 0 Tc 8.5 0 0 8.5 199.76 438.49 Tm (n )Tj /T1_0 1 Tf 0.0382 Tc 8.3 0 0 8.3 228.77 438.49 Tm (necessary )Tj 0.05 Tc 8.9299 0 0 8.3 266.67 438.49 Tm (and )Tj 0.0343 Tc 8.3 0 0 8.3 283.74 438.49 Tm (sufficient )Tj 0.0433 Tc 4.494 0 Td (conditions )Tj 0.0146 Tc -34.852 -1.258 Td (for )Tj 0.05 Tc 8.8795 0 0 8.3 45.16 428.05 Tm (the )Tj 8.3951 0 0 8.3 60.03 428.05 Tm (existence )Tj 8.5556 0 0 8.3 98.2 428.05 Tm (of )Tj 0 Tc 8.3 0 0 8.3 108.28 428.05 Tm (a )Tj /T1_2 1 Tf 0.05 Tc 9.2717 0 0 8.5 115.19 428.05 Tm (GBRD\(v,3,A; )Tj /T1_0 1 Tf 0.0198 Tc 8.3 0 0 8.3 188.27 428.05 Tm (where )Tj -0.0209 Tc 3.81 0 Td (is )Tj 0.05 Tc 8.5465 0 0 8.3 228.7 428.05 Tm (odd )Tj 8.6701 0 0 8.3 245.79 428.05 Tm (are )Tj 0.0288 Tc 8.3 0 0 8.3 260.21 428.05 Tm (given )Tj 0.05 Tc 8.4356 0 0 8.3 283.07 428.05 Tm (in )Tj -0.0192 Tc 8.3 0 0 8.3 293.74 428.05 Tm ([2]. )Tj 0 Tc 10.6 0 0 10.6 32.34 401.41 Tm (2 )Tj 0.05 Tc 13.0088 0 0 10.6 78.73 401.23 Tm (group )Tj /T1_2 1 Tf -0.035 Tc 11.4374 0 0 11.5 117.19 401.23 Tm (Z2t, )Tj 0 Tc 11.5 0 0 11.5 137.2 401.23 Tm (t )Tj /T1_0 1 Tf 10.5 0 0 10.5 145.2 401.23 Tm (E )Tj 0.05 Tc 8.4689 0 0 8.3 32.15 382.87 Tm (Theorem )Tj 0.0459 Tc 8.3 0 0 8.3 74.47 382.87 Tm (2.2 )Tj 0.0317 Tc 2.458 0 Td (below )Tj 0.0475 Tc 3.653 0 Td (eliminates )Tj 0.05 Tc 8.6063 0 0 8.3 171.88 382.87 Tm (the )Tj 0.0313 Tc 8.3 0 0 8.3 192.25 382.87 Tm (possibility )Tj 0.05 Tc 8.5556 0 0 8.3 238.06 382.87 Tm (of )Tj 8.6063 0 0 8.3 253.96 382.87 Tm (the )Tj 8.3951 0 0 8.3 274.23 382.87 Tm (existence )Tj 8.5556 0 0 8.3 318.16 382.87 Tm (of )Tj 8.4715 0 0 8.3 334 382.87 Tm (certain )Tj /T1_2 1 Tf 9.575 0 0 8.5 32.03 372.25 Tm (GBRD\( )Tj /T1_3 1 Tf 6.5511 0 0 5.1 63.54 372.25 Tm (Vj )Tj /T1_2 1 Tf 8.8425 0 0 8.5 71.98 372.25 Tm (k, )Tj -0.035 Tc 7.5728 0 0 8.5 81.3 372.25 Tm (A; )Tj /T1_0 1 Tf 0.05 Tc 9.9514 0 0 8.3 32.35 352.63 Tm (Lemma )Tj 8.7898 0 0 8.3 67.99 352.63 Tm (2.1 )Tj /T1_2 1 Tf 10.1515 0 0 8.5 85.78 352.81 Tm (If )Tj 0.0074 Tc 8.5 0 0 8.5 95.3 352.81 Tm (there )Tj 0 Tc 3.648 -0.021 Td (a )Tj 0.05 Tc 9.3937 0 0 8.5 133.37 352.63 Tm (GBRD\(v,k,A; )Tj 0.0216 Tc 8.5 0 0 8.5 212.84 352.81 Tm (then )Tj 0.0074 Tc 4.786 0 Td (is )Tj 0 Tc 1.086 0 Td (a )Tj 0.05 Tc 9.0815 0 0 8.5 310.48 352.63 Tm (k, )Tj -0.035 Tc 7.1743 0 0 8.5 319.79 352.63 Tm (A; )Tj 0.0338 Tc 8.5 0 0 8.5 328.87 352.63 Tm (Zn\). )Tj /T1_0 1 Tf 0.05 Tc 9.416 0 0 8.3 32.9 323.83 Tm (Proof: )Tj 8.3526 0 0 8.3 65.66 323.83 Tm (Replace )Tj 8.4776 0 0 8.3 318.97 323.83 Tm (by )Tj /T1_2 1 Tf 0 Tc 8.5 0 0 8.5 332.01 323.83 Tm (x )Tj /T1_0 1 Tf 0.05 Tc 8.594 0 0 8.3 340.28 323.83 Tm (\(mod )Tj /T1_2 1 Tf 0.0278 Tc 8.5 0 0 8.5 33.08 313.21 Tm (n\). )Tj /T1_0 1 Tf 0.0415 Tc 8.3 0 0 8.3 47.62 313.21 Tm (Clearly )Tj 0.05 Tc 9.1527 0 0 8.3 77.74 313.21 Tm (the )Tj 8.8342 0 0 8.3 129.22 313.39 Tm (matrix )Tj -0.035 Tc 8.1972 0 0 8.3 157.43 313.39 Tm (is )Tj 0 Tc 8.3 0 0 8.3 166.06 313.39 Tm (a )Tj /T1_2 1 Tf 0.0301 Tc 8.5 0 0 8.5 212.2 313.03 Tm (k,A; )Tj /T1_0 1 Tf 0 Tc 6.8001 0 0 6.8001 354.17 313.75 Tm (0 )Tj 0.05 Tc 9.8572 0 0 8.3 32.86 293.59 Tm (Theorem )Tj 9.0602 0 0 8.3 75.37 293.59 Tm (2.2 )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 93.9 293.77 Tm (A )Tj -0.0054 Tc 8.5 0 0 8.5 103.28 293.77 Tm (necessar'y )Tj 0.0249 Tc 4.529 0 Td (condition )Tj 0.0288 Tc 4.359 0 Td (for )Tj -0.014 Tc 1.714 0 Td (the )Tj 0.05 Tc 9.5923 0 0 8.5 243.64 293.77 Tm (of )Tj 0 Tc 8.5 0 0 8.5 254.11 293.77 Tm (a )Tj 0.05 Tc 8.6035 0 0 8.5 301.84 293.41 Tm (k, )Tj 0.0023 Tc 8.5 0 0 8.5 310.65 293.41 Tm (2ct; )Tj 0.0037 Tc 1.847 0 Td (Z2t\) )Tj 0.0147 Tc 2.218 0 Td (with )Tj -0.0264 Tc 9.1 0 0 9.1 32.83 282.97 Tm (t, )Tj 0 Tc 8.5 0 0 8.5 41.74 282.97 Tm (k )Tj 0.0485 Tc 0.949 0 Td (and )Tj /T1_0 1 Tf 0 Tc 8.1 0 0 8.1 66.52 282.97 Tm (c )Tj /T1_2 1 Tf 0.0224 Tc 8.5 0 0 8.5 73.73 282.97 Tm (odd )Tj 0 Tc 8.1 0 0 8.1 99.67 283.15 Tm (v )Tj /T1_0 1 Tf 12.5 0 0 12.5 115.26 282.97 Tm (o )Tj 0.05 Tc 8.9729 0 0 8.2 123.21 282.97 Tm (or )Tj /T1_2 1 Tf 0.0239 Tc 8.5 0 0 8.5 142.57 282.79 Tm (\(mod )Tj -0.035 Tc 9.364 0 0 10.6 164.08 282.79 Tm (4\). )Tj /T1_0 1 Tf 0.05 Tc 9.416 0 0 8.3 32.72 253.99 Tm (Proof: )Tj 8.7068 0 0 8.3 63.66 253.99 Tm (In )Tj 0.034 Tc 8.3 0 0 8.3 75.04 253.99 Tm (view )Tj 0.05 Tc 8.5556 0 0 8.3 95.68 253.99 Tm (of )Tj 8.5616 0 0 8.3 105.79 253.99 Tm (Lemma )Tj 0.0025 Tc 8.3 0 0 8.3 136.75 253.99 Tm (2.1 )Tj 0.0298 Tc 1.688 0 Td (above )Tj 0.0399 Tc 8.1 0 0 8.1 174.89 253.99 Tm (it )Tj 0.0102 Tc 8.3 0 0 8.3 192.12 253.99 Tm (sufficient )Tj 0.05 Tc 8.731 0 0 8.3 227.86 253.99 Tm (to )Tj 0.0459 Tc 8.3 0 0 8.3 238.33 253.99 Tm (prove )Tj 0.05 Tc 8.6063 0 0 8.3 261.88 253.99 Tm (the )Tj 8.4579 0 0 8.3 276.83 253.99 Tm (result )Tj 0.0363 Tc 8.3 0 0 8.3 301.41 253.99 Tm (for )Tj /T1_1 1 Tf 0 Tc 7.3001 0 0 7.3001 315.42 253.99 Tm (t )Tj /T1_0 1 Tf 12.1 0 0 12.1 321.42 253.99 Tm (= )Tj 8.3 0 0 8.3 330.55 253.99 Tm (1 )Tj 0.0188 Tc 0.784 0 Td (only. )Tj 0.0243 Tc -35.041 -1.236 Td (Let )Tj /T1_2 1 Tf 0 Tc 8.1 0 0 8.1 61.54 243.73 Tm (k )Tj /T1_0 1 Tf 0.05 Tc 8.8124 0 0 8.3 69.03 243.73 Tm (and )Tj 0 Tc 8.3 0 0 8.3 86.32 243.73 Tm (c )Tj 0.05 Tc 8.6029 0 0 8.3 93.25 243.73 Tm (be )Tj 8.4326 0 0 8.3 104.86 243.73 Tm (odd )Tj 8.6949 0 0 8.3 121.77 243.73 Tm (and )Tj 0.0493 Tc 8.3 0 0 8.3 138.66 243.73 Tm (suppose )Tj 0.05 Tc 8.3697 0 0 8.3 171.16 243.73 Tm (there )Tj 0.0067 Tc 8.3 0 0 8.3 271.21 243.73 Tm (2cj )Tj 0.05 Tc 8.5538 0 0 8.3 302.32 243.73 Tm (denote )Tj 8.5737 0 0 8.3 330.23 243.73 Tm (it )Tj /T1_2 1 Tf 9.0929 0 0 8.1 351.25 243.73 Tm (B. )Tj /T1_0 1 Tf 0.0243 Tc 8.3 0 0 8.3 32.9 233.11 Tm (Let )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 48.49 233.11 Tm (B )Tj /T1_0 1 Tf 0.05 Tc 8.7859 0 0 8.3 57.43 233.11 Tm (be )Tj 8.8795 0 0 8.3 69.64 233.11 Tm (the )Tj 8.6674 0 0 8.3 85.38 233.11 Tm (set )Tj 8.5556 0 0 8.3 99.64 233.11 Tm (of )Tj 8.3575 0 0 8.3 109.96 233.11 Tm (matrices, )Tj 8.5556 0 0 8.3 147.16 233.11 Tm (of )Tj 8.6063 0 0 8.3 157.48 233.11 Tm (the )Tj 0.0416 Tc 8.3 0 0 8.3 266.69 233.11 Tm (in )Tj 0.05 Tc 9.0161 0 0 8.3 277.72 233.11 Tm (the )Tj 8.6827 0 0 8.3 293.28 233.11 Tm (same )Tj 0.0434 Tc 8.3 0 0 8.3 315.91 233.11 Tm (positions )Tj 0.0465 Tc 4.413 0 Td (as )Tj /T1_2 1 Tf 0 Tc 8.5 0 0 8.5 33 222.49 Tm (B )Tj /T1_0 1 Tf 0.05 Tc 8.6949 0 0 8.3 42.75 222.49 Tm (and )Tj 8.4914 0 0 8.3 59.67 222.49 Tm (elements )Tj 8.5556 0 0 8.3 96.4 222.49 Tm (of )Tj /T1_2 1 Tf -0.035 Tc 7.9761 0 0 8.5 106.93 222.49 Tm (Z2 )Tj /T1_0 1 Tf 0.0344 Tc 8.3 0 0 8.3 118.89 222.49 Tm (elsewhere. )Tj -0.0348 Tc 5.19 0 Td (We )Tj 0.05 Tc 8.7711 0 0 8.3 255.76 222.49 Tm (matrix )Tj /T1_2 1 Tf 0 Tc 8.5 0 0 8.5 284.67 222.49 Tm (M )Tj /T1_0 1 Tf 8.3 0 0 8.3 296.95 222.49 Tm (E )Tj /T1_2 1 Tf 8.6 0 0 8.6 305.52 222.49 Tm (B )Tj /T1_0 1 Tf 8.3 0 0 8.3 314.74 222.49 Tm (a )Tj /T1_3 1 Tf -0.035 Tc 8.1327 0 0 12.8 350.34 222.49 Tm (G\) )Tj /T1_0 1 Tf 0.0385 Tc 8.3 0 0 8.3 32.66 212.05 Tm (-vector )Tj 0.05 Tc 8.4736 0 0 8.3 85.59 212.05 Tm (as )Tj 0.0011 Tc 8.3 0 0 8.3 96.57 212.05 Tm (follows. )Tj 0.0351 Tc 3.888 0 Td (Let )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 144.82 212.05 Tm (M )Tj /T1_0 1 Tf 8.3 0 0 8.3 156.55 212.05 Tm (E )Tj /T1_2 1 Tf -0.035 Tc 8.9389 0 0 9.2 164.23 212.05 Tm (B. )Tj /T1_0 1 Tf 0.0306 Tc 8.3 0 0 8.3 32.57 174.07 Tm (where )Tj 0.05 Tc 8.7429 0 0 8.3 57.4 174.07 Tm (the )Tj /T1_1 1 Tf 8.0422 0 0 6.2 72.44 174.07 Tm (ai )Tj /T1_0 1 Tf 8.8078 0 0 8.3 83.07 174.07 Tm (are )Tj 0.0234 Tc 8.3 0 0 8.3 97.85 174.07 Tm (given )Tj 0.05 Tc 8.4776 0 0 8.3 120.79 174.07 Tm (by )Tj 0.0366 Tc 8.3 0 0 8.3 32.72 135.73 Tm (Label )Tj 0.05 Tc 8.7429 0 0 8.3 55.96 135.73 Tm (the )Tj 8.5584 0 0 8.3 71.02 135.73 Tm (distinct )Tj 8.4109 0 0 8.3 102.78 135.73 Tm (unordered )Tj 0.0481 Tc 8.3 0 0 8.3 143.83 135.73 Tm (pairs )Tj 0.05 Tc 8.5556 0 0 8.3 164.62 135.73 Tm (of )Tj 0.0027 Tc 8.3 0 0 8.3 174.41 135.73 Tm (rows )Tj 0.05 Tc 8.3469 0 0 8.3 193.6 135.73 Tm (of )Tj /T1_2 1 Tf 0 Tc 8.8 0 0 8.8 203.49 135.73 Tm (M )Tj /T1_0 1 Tf 0.0289 Tc 8.3 0 0 8.3 214.93 135.73 Tm (by )Tj /T1_2 1 Tf 0.05 Tc 9.0368 0 0 8.8 226.15 135.73 Tm (Pl\(M\),P2\(M\), )Tj 9.6295 0 0 8.8 283.41 135.73 Tm (.. )Tj 11.0161 0 0 8.8 290.95 135.73 Tm ("pcn\(M\) )Tj /T1_0 1 Tf 0.0432 Tc 8.3 0 0 8.3 334.88 135.73 Tm (\(where )Tj 0.05 Tc 8.4697 0 0 8.3 32.56 123.31 Tm (the )Tj 8.3325 0 0 8.3 47.26 123.31 Tm (ordering )Tj 0.0008 Tc 8.3 0 0 8.3 81.65 123.31 Tm (is )Tj 0.05 Tc 8.7429 0 0 8.3 91.06 123.31 Tm (the )Tj 8.352 0 0 8.3 106.08 123.31 Tm (same )Tj 0.0038 Tc 8.3 0 0 8.3 127.71 123.31 Tm (for )Tj 0.0058 Tc 1.649 0 Td (all )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 153.64 123.31 Tm (M )Tj /T1_0 1 Tf 8.3 0 0 8.3 165.55 123.31 Tm (E )Tj /T1_2 1 Tf -0.0196 Tc 9.2 0 0 9.2 173.23 123.31 Tm (B\). )Tj /T1_0 1 Tf 0.0062 Tc 8.3 0 0 8.3 188.42 123.31 Tm (Define )Tj /T1_1 1 Tf 0.05 Tc 8.9665 0 0 8.6 214.44 123.31 Tm (4\(M\) )Tj /T1_0 1 Tf 0.0289 Tc 8.3 0 0 8.3 237.97 123.31 Tm (by )Tj 0 Tc 8.1 0 0 8.1 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-0.0115 Tc 2.661 0 Td (size )Tj 0.0232 Tc 1.882 0 Td (4. )Tj /T1_2 1 Tf 0.05 Tc 8.478 0 0 7.1 44.41 336.79 Tm (AMS )Tj 7.1989 0 0 7.1 64.43 336.79 Tm (Subject )Tj 0.0423 Tc 7.1 0 0 7.1 91.3 336.79 Tm (Classification: )Tj /T1_0 1 Tf 0.0021 Tc 7.6 0 0 7.6 141.76 336.79 Tm (05B99 )Tj /T1_3 1 Tf 0.05 Tc 6.7204 0 0 5.6 44.4 327.61 Tm (J\( )Tj /T1_2 1 Tf 0.0401 Tc 7.1 0 0 7.1 50.7 327.61 Tm (ey )Tj 0.0371 Tc 1.424 0 Td (words )Tj 0.0403 Tc 3.092 0 Td (and )Tj 0.0442 Tc 2.017 0 Td (phrases: )Tj /T1_0 1 Tf 7.6 0 0 7.6 127.59 327.61 Tm (Balanced )Tj 0.05 Tc 7.7066 0 0 7.6 160.87 327.61 Tm (Incomplete )Tj 0.0128 Tc 7.6 0 0 7.6 202.11 327.61 Tm (Block )Tj 0.0069 Tc 2.842 0 Td (Designs; )Tj 0.0432 Tc 3.996 0 Td (Generalised )Tj 0.0382 Tc 5.62 0 Td (Bhaskar )Tj 0.05 Tc 7.6991 0 0 7.6 44.25 318.61 Tm (Rao )Tj 0.0227 Tc 7.6 0 0 7.6 60.45 318.61 Tm (Designs )Tj 0 Tc 11 0 0 11 22.66 291.97 Tm (1 )Tj 0.05 Tc 12.8541 0 0 11 42.21 291.97 Tm (Introduction )Tj 0 Tc 8.3 0 0 8.3 22.49 273.25 Tm (A )Tj /T1_2 1 Tf 0.0281 Tc 8.2 0 0 8.2 32.18 273.25 Tm (design )Tj /T1_0 1 Tf -0.0209 Tc 8.3 0 0 8.3 57.89 273.25 Tm (is )Tj 0 Tc 1.061 0 Td (a )Tj 0.0492 Tc 0.813 0 Td (pair )Tj /T1_2 1 Tf 0.05 Tc 9.0579 0 0 8.2 105.19 273.25 Tm (B\) )Tj /T1_0 1 Tf 0.0469 Tc 8.3 0 0 8.3 117.53 273.25 Tm (where )Tj 0 Tc 2.993 0 Td (X )Tj -0.035 Tc 8.1972 0 0 8.3 152.39 273.25 Tm (is )Tj 0 Tc 8.3 0 0 8.3 160.66 273.25 Tm (a )Tj 0.0258 Tc 0.823 0 Td (finite )Tj 0.0437 Tc 2.664 0 Td (set )Tj 0.05 Tc 8.3469 0 0 8.3 202.6 273.25 Tm (of )Tj /T1_2 1 Tf 8.3174 0 0 8.2 212.69 273.25 Tm (elements )Tj /T1_0 1 Tf 8.5774 0 0 8.3 247.59 273.25 Tm (and )Tj /T1_2 1 Tf 0 Tc 8.2 0 0 8.2 264.3 273.25 Tm (B )Tj /T1_0 1 Tf -0.0209 Tc 8.3 0 0 8.3 273.89 273.25 Tm (is )Tj 0 Tc 1.018 0 Td (a )Tj 0.0172 Tc 0.801 0 Td (finite )Tj 0.0298 Tc 2.582 0 Td (collection )Tj 0.05 Tc 8.3469 0 0 8.3 22.24 262.81 Tm (of )Tj 8.4775 0 0 8.3 32.84 262.81 Tm (\(not )Tj 0.0207 Tc 8.3 0 0 8.3 51.47 262.81 Tm (necessarily )Tj 0.0474 Tc 5.131 0 Td (distinct\) )Tj 0.0435 Tc 4.181 0 Td (subsets )Tj 0.0348 Tc 3.581 0 Td (\(called )Tj 0.0281 Tc 3.396 0 Td (blocks\) )Tj 0.05 Tc 8.5556 0 0 8.3 216.1 262.81 Tm (of )Tj 9.2098 0 0 8.6 226.42 262.81 Tm (X. )Tj 0 Tc 8.6 0 0 8.6 241.18 262.81 Tm (A )Tj /T1_2 1 Tf 0.0159 Tc 8.2 0 0 8.2 251.04 262.81 Tm (balanced )Tj 0.0345 Tc 4.188 0 Td (incomplete )Tj -0.0032 Tc 5.251 0 Td (block )Tj 0.0256 Tc -37.249 -1.295 Td (design, )Tj 0.05 Tc 9.1047 0 0 8.2 51.55 252.19 Tm (BIBD\(v,b,r,k,>.\), )Tj /T1_0 1 Tf -0.0209 Tc 8.3 0 0 8.3 124.85 252.19 Tm (is )Tj 0 Tc 1.061 0 Td (a )Tj 0.0178 Tc 0.889 0 Td (design )Tj 0.05 Tc 8.4307 0 0 8.3 167.21 252.19 Tm (with )Tj /T1_2 1 Tf 0 Tc 8.2 0 0 8.2 187.15 252.19 Tm (v )Tj /T1_0 1 Tf 0.0411 Tc 8.3 0 0 8.3 194.13 252.19 Tm (elements )Tj 0.05 Tc 8.4599 0 0 8.3 229.41 252.19 Tm (and )Tj /T1_2 1 Tf 0 Tc 8.2 0 0 8.2 246 252.19 Tm (b )Tj /T1_0 1 Tf 0.044 Tc 8.3 0 0 8.3 252.19 252.19 Tm (blocks )Tj 0.0267 Tc 3.216 0 Td (such )Tj 0.05 Tc 8.9746 0 0 8.3 298.24 252.19 Tm (that )Tj 0.0193 Tc 8.6 0 0 8.6 30.68 235.09 Tm (\(i\) )Tj 0.0331 Tc 8.3 0 0 8.3 44.01 235.09 Tm (each )Tj 0.0296 Tc 2.32 0 Td (element )Tj 0.05 Tc 8.4613 0 0 8.3 94.59 235.09 Tm (appears )Tj 0.0416 Tc 8.3 0 0 8.3 126.29 235.09 Tm (in )Tj 0.0433 Tc 1.234 0 Td (exactly )Tj /T1_3 1 Tf 0 Tc 6.9001 0 0 6.9001 166.08 235.09 Tm (r )Tj /T1_0 1 Tf 0.031 Tc 8.3 0 0 8.3 173.17 235.09 Tm (blocks )Tj -0.0137 Tc 9 0 0 9 28.51 217.63 Tm (\(ii\) )Tj 0.0331 Tc 8.3 0 0 8.3 44.01 217.63 Tm (each )Tj 0.0221 Tc 2.354 0 Td (block )Tj 0.0354 Tc 2.7 0 Td (contains )Tj 0.05 Tc 8.308 0 0 8.3 119.07 217.63 Tm (exactly )Tj /C0_0 1 Tf 0 Tc 4.5001 0 0 6.4801 149.23 217.63 Tm <006B0028007E0020>Tj /T1_3 1 Tf -0.035 Tc 8.6356 0 0 8.7 166.3 217.63 Tm (v\) )Tj /T1_0 1 Tf 0.05 Tc 8.3058 0 0 8.3 176.67 217.63 Tm (elements )Tj 0.0154 Tc 8.3 0 0 8.3 26 200.35 Tm (\(iii\) )Tj 0.0331 Tc 2.17 0 Td (each )Tj 0.0492 Tc 2.333 0 Td (pair )Tj 0.0332 Tc 2.114 0 Td (of )Tj 0.0429 Tc 1.149 0 Td (distinct )Tj 0.0442 Tc 3.707 0 Td (elements )Tj 0.05 Tc 8.5691 0 0 8.3 156.51 200.35 Tm (appears )Tj 0.0416 Tc 8.3 0 0 8.3 188.39 200.35 Tm (in )Tj 0.05 Tc 8.3018 0 0 8.3 198.63 200.35 Tm (exactly>. )Tj 0.0136 Tc 8.3 0 0 8.3 236.17 200.35 Tm (blocks )Tj 0.0069 Tc -24.07 -2.125 Td (Since )Tj /T1_2 1 Tf 0.0034 Tc 8.7 0 0 8.7 58.81 182.71 Tm (r\( )Tj 0 Tc 8.4 0 0 8.4 66.22 182.71 Tm (k )Tj /T1_0 1 Tf 0.826 0 Td (-)Tj /T1_1 1 Tf -0.035 Tc 7.9859 0 0 8.9 81.64 182.71 Tm (1\) )Tj /T1_0 1 Tf 6.5959 0 0 8.3 100.77 182.71 Tm (>.\( )Tj /T1_2 1 Tf 0 Tc 8.7 0 0 8.7 108.85 182.71 Tm (v )Tj /T1_1 1 Tf -0.035 Tc 8.2208 0 0 8.9 123.76 182.71 Tm (1\) )Tj /T1_0 1 Tf 0.05 Tc 8.4599 0 0 8.3 134.19 182.71 Tm (and )Tj /T1_2 1 Tf 0.0231 Tc 8.7 0 0 8.7 151.15 182.71 Tm (vr )Tj /T1_0 1 Tf 0 Tc 12.1 0 0 12.1 162.12 182.71 Tm (= )Tj /T1_2 1 Tf -0.0007 Tc 8.4 0 0 8.4 171.3 182.71 Tm (bk )Tj /T1_0 1 Tf 0.05 Tc 8.3949 0 0 8.3 182.8 182.71 Tm (are )Tj 0.017 Tc 8.3 0 0 8.3 197.27 182.71 Tm (well-known )Tj 0.0437 Tc 5.357 0 Td (necessary )Tj 0.0312 Tc 4.611 0 Td (conditions )Tj 0.0363 Tc 4.835 0 Td (for )Tj 0.05 Tc 8.7429 0 0 8.3 334.24 182.71 Tm (the )Tj 0.0369 Tc 8.3 0 0 8.3 22.23 172.09 Tm (existence )Tj 0.05 Tc 8.5556 0 0 8.3 58.96 172.09 Tm (of )Tj 0 Tc 8.3 0 0 8.3 69.04 172.09 Tm (a )Tj /T1_2 1 Tf 0.05 Tc 10.5072 0 0 8.2 76.4 172.09 Tm (BI )Tj 9.2773 0 0 8.2 87.55 172.09 Tm (BD\( )Tj 0.0163 Tc 8.2 0 0 8.2 105.07 172.09 Tm (v, )Tj -0.035 Tc 7.7794 0 0 8.2 112.8 172.09 Tm (b, )Tj 0.0208 Tc 8.2 0 0 8.2 120.55 172.09 Tm (r, )Tj 0.05 Tc 8.6035 0 0 8.2 127.96 172.09 Tm (k, )Tj /T1_0 1 Tf -0.035 Tc 6.9341 0 0 8.3 136.95 172.09 Tm (>.\) )Tj 7.9961 0 0 8.3 147.77 172.09 Tm (we )Tj 0.05 Tc 8.4918 0 0 8.3 160.12 172.09 Tm (denote )Tj 0.0475 Tc 8.3 0 0 8.3 188.26 172.09 Tm (this )Tj 0.0072 Tc 5.187 0 Td (by )Tj /T1_2 1 Tf 0.05 Tc 10.6884 0 0 8.2 243.44 172.09 Tm (BI )Tj 9.5831 0 0 8.2 254.59 172.09 Tm (BD\( )Tj 0.0382 Tc 8.2 0 0 8.2 272.65 172.09 Tm (v, )Tj 0.05 Tc 8.3645 0 0 8.2 280.96 172.09 Tm (k, )Tj /T1_0 1 Tf -0.035 Tc 7.4572 0 0 8.3 289.58 172.09 Tm (>.\). )Tj 0.0134 Tc 8.3 0 0 8.3 36.32 161.65 Tm (Let )Tj /T1_3 1 Tf 0 Tc 7.9001 0 0 7.9001 51.61 161.65 Tm (G )Tj /T1_0 1 Tf 0.0208 Tc 8.3 0 0 8.3 61.57 161.65 Tm (be )Tj 0 Tc 1.42 0 Td (a )Tj 0.0128 Tc 0.866 0 Td (finite )Tj 0.0439 Tc 2.627 0 Td (group )Tj 0.05 Tc 8.3371 0 0 8.3 127.25 161.65 Tm (with )Tj 8.4022 0 0 8.3 146.63 161.65 Tm (identity )Tj /T1_2 1 Tf 0.0009 Tc 8.2 0 0 8.2 179.21 161.65 Tm (e, )Tj /T1_0 1 Tf 0.05 Tc 8.4599 0 0 8.3 188.73 161.65 Tm (and )Tj 0.0296 Tc 8.3 0 0 8.3 205.49 161.65 Tm (let )Tj /T1_3 1 Tf 0.05 Tc 8.6953 0 0 7.9001 218.46 161.65 Tm (Z\( )Tj 8.1433 0 0 7.9001 228.01 161.65 Tm (G\) )Tj /T1_0 1 Tf 8.4199 0 0 8.3 241.03 161.65 Tm (be )Tj 8.7429 0 0 8.3 252.7 161.65 Tm (the )Tj 8.4343 0 0 8.3 267.77 161.65 Tm (group )Tj 0.0273 Tc 8.3 0 0 8.3 292.67 161.65 Tm (ring )Tj 0.0332 Tc 2.139 0 Td (of )Tj 0.05 Tc 9.4598 0 0 8.3 320.13 161.65 Tm (Gover )Tj 8.7429 0 0 8.3 22.48 151.03 Tm (the )Tj 0.0345 Tc 8.3 0 0 8.3 37.79 151.03 Tm (ring )Tj 0.05 Tc 8.3469 0 0 8.3 55.54 151.03 Tm (of )Tj 0.0339 Tc 8.3 0 0 8.3 65.27 151.03 Tm (integers )Tj /T1_2 1 Tf 0.05 Tc 8.4527 0 0 8.2 97.75 151.03 Tm (Z. )Tj /T1_1 1 Tf 0 Tc 7.9001 0 0 7.9001 110.35 151.03 Tm (A )Tj /T1_2 1 Tf 0.0264 Tc 8.2 0 0 8.2 120.13 151.03 Tm (generalised )Tj 0.05 Tc 8.4261 0 0 8.2 164.04 151.03 Tm (Bhaskar )Tj 0.0416 Tc 8.2 0 0 8.2 198.24 151.03 Tm (Rao )Tj 0.0281 Tc 2.139 0 Td (design )Tj 0.027 Tc 3.278 0 Td (\(with )Tj 0.05 Tc 8.6283 0 0 8.2 264.35 151.03 Tm (one )Tj 0.0308 Tc 8.2 0 0 8.2 281.29 151.03 Tm (association )Tj 0.0414 Tc 5.377 0 Td (class\) )Tj /T1_0 1 Tf 0.05 Tc 8.4307 0 0 8.3 22.31 140.59 Tm (with )Tj 8.511 0 0 8.3 42.49 140.59 Tm (parameters )Tj /T1_2 1 Tf 0.0382 Tc 8.2 0 0 8.2 86.89 140.59 Tm (v, )Tj -0.035 Tc 8.0387 0 0 8.8 94.98 140.59 Tm (b, )Tj -0.0231 Tc 8.2 0 0 8.2 102.73 140.59 Tm (r, )Tj 0.0127 Tc 8.8 0 0 8.8 109.96 140.59 Tm (k, )Tj /T1_0 1 Tf -0.035 Tc 5.4026 0 0 8.3 118.6 140.59 Tm (>. )Tj 0.05 Tc 8.5774 0 0 8.3 126.81 140.59 Tm (and )Tj /T1_2 1 Tf 0 Tc 8.8 0 0 8.8 143.64 140.59 Tm (G )Tj /T1_0 1 Tf -0.035 Tc 8.1972 0 0 8.3 153.29 140.59 Tm (is )Tj 0 Tc 8.3 0 0 8.3 162.28 140.59 Tm (a )Tj /T1_2 1 Tf 8.2 0 0 8.2 170.23 140.59 Tm (v )Tj /T1_1 1 Tf 6.1 0 0 6.1 177.66 140.59 Tm (X )Tj /T1_2 1 Tf 8.8 0 0 8.8 185.7 140.59 Tm (b )Tj /T1_0 1 Tf 0.05 Tc 8.6449 0 0 8.3 192.4 140.59 Tm (matrix )Tj 8.3371 0 0 8.3 220.67 140.59 Tm (with )Tj 0.0367 Tc 8.3 0 0 8.3 240.21 140.59 Tm (entries )Tj 0.05 Tc 8.3515 0 0 8.3 267.57 140.59 Tm (from )Tj /T1_2 1 Tf 0 Tc 8.8 0 0 8.8 288.9 140.59 Tm (G )Tj /T1_1 1 Tf 8.9 0 0 8.9 297.91 140.59 Tm (u )Tj 0.0381 Tc 0.861 0 Td ({a}, )Tj /T1_0 1 Tf 0.0469 Tc 8.3 0 0 8.3 323.81 140.59 Tm (where )Tj 0 Tc 12.1 0 0 12.1 22.38 130.15 Tm (o )Tj /T1_2 1 Tf -0.035 Tc 5.8813 0 0 9.4 29.67 130.15 Tm (rJ )Tj /T1_3 1 Tf -0.002 Tc 8.3 0 0 8.3 37.38 130.15 Tm (G, )Tj /T1_0 1 Tf 0.0267 Tc 1.446 0 Td (such )Tj 0.05 Tc 9.084 0 0 8.3 68.74 130.15 Tm (that )Tj /T1_1 1 Tf 6.8474 0 0 6.3001 187.44 122.95 Tm (\), )Tj /T1_3 1 Tf 0.0288 Tc 11 0 0 11 124.13 115.39 Tm (ww+ )Tj /T1_1 1 Tf 0 Tc 8.1 0 0 8.1 151.07 115.39 Tm (= )Tj /T1_2 1 Tf 0.05 Tc 9.8279 0 0 8.7 159.78 115.39 Tm (reI )Tj /T1_1 1 Tf 0 Tc 11.7 0 0 11.7 174.41 115.39 Tm (+ )Tj -0.035 Tc 7.4176 0 0 13.4 183.94 115.39 Tm (fGT )Tj 0 Tc 14.9 0 0 14.9 198.94 115.39 Tm (L )Tj /T1_2 1 Tf -0.035 Tc 8.8622 0 0 9.2 212.3 115.39 Tm (g\( )Tj /T1_3 1 Tf 0 Tc 8.4 0 0 8.4 220.42 115.39 Tm (J )Tj /T1_1 1 Tf 0.923 0 Td (-)Tj /T1_2 1 Tf 0.05 Tc 9.391 0 0 8.7 236.25 115.39 Tm (I\) )Tj 6.5659 0 0 5.9001 197.7 106.39 Tm (gEG )Tj /T1_1 1 Tf -0.0033 Tc 8.8 0 0 8.8 335.01 115.39 Tm (\(1\) )Tj /T1_0 1 Tf 0.036 Tc 8.3 0 0 8.3 22.31 91.99 Tm (where )Tj /T1_3 1 Tf -0.035 Tc 7.2598 0 0 7.9001 47.79 91.99 Tm (VV+ )Tj /T1_0 1 Tf 8.1972 0 0 8.3 65.63 91.99 Tm (is )Tj 0.05 Tc 8.3331 0 0 8.3 75.04 91.99 Tm (the )Tj 8.4571 0 0 8.3 89.62 91.99 Tm (transpose )Tj 8.3469 0 0 8.3 128.44 91.99 Tm (of )Tj /T1_3 1 Tf 0 Tc 7.9001 0 0 7.9001 138.67 91.99 Tm (W )Tj /T1_0 1 Tf 0.05 Tc 8.4307 0 0 8.3 151.37 91.99 Tm (with )Tj 8.8795 0 0 8.3 171.34 91.99 Tm (the )Tj 0.0493 Tc 8.3 0 0 8.3 186.77 91.99 Tm (group )Tj 0.038 Tc 2.99 0 Td (elements )Tj 0.0467 Tc 4.239 0 Td (replaced )Tj 0.05 Tc 8.3046 0 0 8.3 281.35 91.99 Tm (by )Tj 8.3447 0 0 8.3 293.56 91.99 Tm (their )Tj 0.0305 Tc 8.3 0 0 8.3 314.21 91.99 Tm (inverses, )Tj 0.05 Tc 8.6949 0 0 8.3 22.23 81.36 Tm (and )Tj 8.6063 0 0 8.3 39.22 81.36 Tm (the )Tj 8.5048 0 0 8.3 53.83 81.36 Tm (product )Tj /T1_3 1 Tf 8.7669 0 0 7.9001 85.9 81.36 Tm (WW+ )Tj /T1_0 1 Tf -0.035 Tc 7.9044 0 0 8.3 112.44 81.36 Tm (is )Tj 0.0474 Tc 8.3 0 0 8.3 121.23 81.36 Tm (evaluated )Tj 0.05 Tc 8.4356 0 0 8.3 159.41 81.36 Tm (in )Tj /T1_3 1 Tf 8.6953 0 0 7.9001 170.4 81.36 Tm (Z\( )Tj 8.1688 0 0 7.9001 179.77 81.36 Tm (G\). )Tj /T1_0 1 Tf 9.9473 0 0 8.6 60.28 58.69 Tm (Australasian )Tj 9.9634 0 0 8.6 120.9 58.69 Tm (Journal )Tj 10.4336 0 0 8.3 158.48 58.69 Tm (of )Tj 9.3338 0 0 8.6 172.88 58.69 Tm (Combinatorics )Tj 9.0812 0 0 8.6 239.11 58.69 Tm (3\(1991\) 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