Abstract

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.

中文翻译：

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满足Runge条件的四度Diophantine方程族的求解算法

摘要

本文针对两个未知数中的一阶四次丢番图方程组，提出了Runge方法基本版本的算法实现。任何四阶Diophantine方程（其前导同质部分分解为线性多项式和三次多项式的乘积）都可以简化为本文考虑的类型的方程。相应的算法（处于优化版本）在PARI / GP计算机代数系统中实现。