An Algorithm for Solving a Family of Fourth-Degree Diophantine Equations that Satisfy Runge’s Condition


This paper proposes an algorithmic implementation of the elementary version of Runge’s method for a family of fourth-degree Diophantine equations in two unknowns. Any Diophantine equation of the fourth degree the leading homogeneous part of which is decomposed into a product of linear and cubic polynomials can be reduced to equations of the type considered in this paper. The corresponding algorithm (in its optimized version) is implemented in the PARI/GP computer algebra system.

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This work was supported by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (agreement no. 075-02-2020-1534/1).

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Correspondence to N. N. Osipov or A. A. Kytmanov.

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Translated by Yu. Kornienko

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Osipov, N.N., Kytmanov, A.A. An Algorithm for Solving a Family of Fourth-Degree Diophantine Equations that Satisfy Runge’s Condition. Program Comput Soft 47, 29–33 (2021).

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