关于一次同余方程组的注记  

Notes on Systems of Linear Congruence Equations

作　　者：石文章 刘合国 Shi Wenzhang;Liu Heguo(School of Mathematics and Statistics,Hubei University,Wuhan 430062,China;School of Mathematics and Statistics,Hainan University,Haikou 570228,China)

机构地区：[1]湖北大学数学与统计学学院,武汉430062 [2]海南大学数学与统计学院,海口570228

出　　处：《数学理论与应用》2023年第4期29-47,共19页Mathematical Theory and Applications

基　　金：国家自然科学基金项目(No.12171142)资助。

摘　　要：中国剩余定理是数论的一条基本原理.本文从整数矩阵在模变换下的标准形入手,给出中国剩余定理的另一证明,然后利用不变因子给出两类多元一次同余方程组有解的充要条件,并在有解时给出解的个数.The Chinese Remainder Theorem is a fundamental principle in number theory. In this paper we start with the canonical form of integer matrix under modular transformations and give another proof to the Chinese Remainder Theorem. Then by using the invariant factors we give some sufficient and necessary conditions for the existence of solutions for two classes of systems of linear congruence equations with multiple variables, and further more, find the number of solutions to the systems.

关 键 词：中国剩余定理 同余 模变换 标准形 不变因子 

分 类 号：O156[理学—数学]