Dong Guizhen. A SUFFICIENT AND NECESSARY CONDITION THAT LINEAR EQUATIONS SYSTEM WITH INTEGRAL COEFFICIENT HAS INTEGRAL SOLUTION[J]. Journal of University of Jinan(Social Science Edition), 1997,(3):59-61.
Dong Guizhen. A SUFFICIENT AND NECESSARY CONDITION THAT LINEAR EQUATIONS SYSTEM WITH INTEGRAL COEFFICIENT HAS INTEGRAL SOLUTION[J]. Journal of University of Jinan(Social Science Edition), 1997,(3):59-61.DOI:
整数环上线性方程组有解的充要条件
摘要
本文利用整数环上矩阵的不变因子理论
给出并证明了整系数线性方程组有整数解的一个充要条件.
Abstract
In this paper
we prove that a sufficient and necessary condition that linear equations system with integral coefficient has integral solutions.
关键词
整数矩阵不变因子正规形式单模矩阵
Keywords
Integral matrixInvariant factorNormal formUnimodular matrix