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An Algorithm for Solving a Quartic Diophantine Equation Satisfying Runge’s Condition

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Computer Algebra in Scientific Computing (CASC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11661))

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Abstract

In this paper, we suggest an implementation of elementary version of Runge’s method for solving a family of diophantine equations of degree four. Moreover, the corresponding solving algorithm (in its optimized version) is implemented in the computer algebra system PARI/GP.

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References

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Author information

Authors and Affiliations

  1. Siberian Federal University, Svobodny 79, Krasnoyarsk, 660041, Russia

    N. N. Osipov & S. D. Dalinkevich

Authors
  1. N. N. Osipov
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  2. S. D. Dalinkevich
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Corresponding author

Correspondence to N. N. Osipov .

Editor information

Editors and Affiliations

  1. Coventry University, Coventry, UK

    Matthew England

  2. University of Kassel, Kassel, Germany

    Wolfram Koepf

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. University of Kassel, Kassel, Germany

    Werner M. Seiler

  5. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Osipov, N.N., Dalinkevich, S.D. (2019). An Algorithm for Solving a Quartic Diophantine Equation Satisfying Runge’s Condition. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_25

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  • DOI: https://doi.org/10.1007/978-3-030-26831-2_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26830-5

  • Online ISBN: 978-3-030-26831-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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