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J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 2, Pages 137–147 (Mi jsfu662)  
This article is cited in 2 scientific papers (total in 3 papers)

An algorithmic implementation of Runge's method for cubic diophantine equations

Nikolay N. Osipov, Bella V. Gulnova

Institute of Space and Information Technology, Siberian Federal University, Kirensky, 26, Krasnoyarsk, 660074, Russia

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.

DOI: https://doi.org/10.17516/1997-1397-2018-11-2-137-147

Full text: PDF file (119 kB)
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Bibliographic databases:

UDC: 511.52
Received: 18.10.2017
Received in revised form: 21.11.2017
Accepted: 18.01.2018
Language:

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

Citation in format AMSBIB
\Bibitem{OsiGul18}
\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}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000434678300002}


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    Citing articles on Google Scholar: Russian citations, English citations
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    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 articles:
    1. 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  mathnet  crossref
    2. Nikolay N. Osipov, Bella V. Gulnova, “Errata to our article”, Zhurn. SFU. Ser. Matem. i fiz., 12:1 (2019), 130–130  mathnet
    3. 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  crossref  mathscinet  zmath  isi  scopus
    		• Журнал Сибирского федерального университета. Серия "Математика и физика"
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