Abstract:
In this paper we propose an algorithmic implementation of the elementary version of Runge's method for solving cubic diophantine equations with two unknowns. Moreover, we give the estimates for the solutions to such equations.
Keywords:
diophantine equations, Runge's method.
Received: 18.10.2017 Received in revised form: 21.11.2017 Accepted: 18.01.2018
Bibliographic databases:
Document Type:
Article
UDC:
511.52
Language: English
Citation:
Nikolay N. Osipov, Bella V. Gulnova, “An algorithmic implementation of Runge's method for cubic diophantine equations”, J. Sib. Fed. Univ. Math. Phys., 11:2 (2018), 137–147
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\by Nikolay~N.~Osipov, Bella~V.~Gulnova
\paper An algorithmic implementation of Runge's method for cubic diophantine equations
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2018
\vol 11
\issue 2
\pages 137--147
\mathnet{http://mi.mathnet.ru/jsfu662}
\crossref{https://doi.org/10.17516/1997-1397-2018-11-2-137-147}
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Linking options:
https://www.mathnet.ru/eng/jsfu662
https://www.mathnet.ru/eng/jsfu/v11/i2/p137
Erratum
Errata to our article Nikolay N. Osipov, Bella V. Gulnova J. Sib. Fed. Univ. Math. Phys., 2019, 12:1, 130
This publication is cited in the following 4 articles:
N. N. Osipov, A. A. Kytmanov, “An algorithm for solving a family of fourth-degree Diophantine equations that satisfy Runge's condition”, Program. Comput. Softw., 47:1 (2021), 29–33
Nikolai N. Osipov, Maria I. Medvedeva, “An elementary algorithm for solving a diophantine equation of degree four with Runge's condition”, Zhurn. SFU. Ser. Matem. i fiz., 12:3 (2019), 331–341
Nikolay N. Osipov, Bella V. Gulnova, “Errata to our article”, Zhurn. SFU. Ser. Matem. i fiz., 12:1 (2019), 130–130
N. N. Osipov, S. D. Dalinkevich, “An algorithm for solving a quartic diophantine equation satisfying Runge's condition”, Computer Algebra in Scientific Computing (Casc 2019), Lecture Notes in Computer Science, 11661, ed. M. England, W. Koepf, T. Sadykov, W. Seiler, E. Vorozhtsov, Springer, 2019, 377–392
Citation in format AMSBIB
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