模m矩阵的广义逆与孙子定理

The Generalized Inverse of A Matrix Modulo m And The Chinese Remainder Theorem

讨论模m矩阵的广义逆,并以此为工具证明了孙子定理,得到了求解一次同余方程组的两种新方法.第一种方法避开了传统解法中分别求"乘率"的做法,第二种方法可直接应用于模数两两未必互素情形下的方程组.

Using the relatively theory to discuss the inverse of matrix modulo m proved the Chinese Remainder Theorem. In this process, two new methods for solving system of congruences were obtained. The first method avoided the inverse for every integer modulo ; the second method could be directly applied to system of congruences with different mod- ulus in which there might be two integers not being relatively prime.