求解丢番图线性方程和方程组的迭代算法
Integer Algorithms to Solver Diophantine Linear Equations and Systems
摘要：
本文的工作包含了作者对丢番图线性方程组的整数解的一些原创性研究。将二元丢番图线性方程的“广义整数解”概念推广到$n$元丢番图线性方程组，进而推广到丢番图线性系.确定了一般整数解的性质（对于丢番图线性方程和丢番图线性系）。给出了七个原始整数算法（丢番图线性方程的两个，丢番图线性系的五个）。对算法进行了严格的证明，并分别给出了一个例子。这些算法可以很容易地在计算机上实现。
英文摘要：
The present work includes some of the author's original researches on integer solutions of Diophantine liner equations and systems. The notion of "general integer solution" of a Diophantine linear equation with two unknowns is extended to Diophantine linear equations with $n$ unknowns and then to Diophantine linear systems. The proprieties of the general integer solution are determined (both for a Diophantine linear equation and for a Diophantine linear system). Seven original integer algorithms (two for Diophantine linear equations, and five for Diophantine linear systems) are exposed. The algorithms are strictly proved and an example for each of them is given. These algorithms can be easily implemented on the computer.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
