一次同余方程组的一种矩阵解法

The Matrix Method of Solving System of Linear Congruence Equations

同余方程组是数论中一个极为有用的课题。文中考虑的是具有一个未知数而具有不同的模的一次同余方程组。一般可以用中国剩余定理或者递推算法等方法给出一次同余方程组的解法。利用矩阵的初等变换和矩阵的Sm ith标准形给出了求解一次同余方程组的一种矩阵解法。

The topic of system of lit.ear congruence equations is extremely useful ha number theory. This article considers system of linear congruence equations of which invotving one variable, but different module. The solution of system of linear congruence equations can be provided by the Chinese remainder theorem or recursive process. The article gives a new method hatroduced for sotving system of linear congruence equations by matrix, elementary transformation and the Smith normal form of matrices.