一次同余式组的逐步逼近解法

Successive Approach Method of a Congruence System of First Degree

以往用剩余定理求解一次同余式组需要反复使用辗转相除法和连乘,计算量很大,且兼容性差,如果式组中增加一个式子则求解需重新开始,原来的计算结果无法利用。本文中提出一种新的求解方法——逐步逼近法,首先选择适当的数使第1,2两式成立,再推出满足前3,4,…,i 个式子的数;以此类推,最后得到式组的解。这种方法比以往方法可省去大量计算,且计算过程具有外延性,十分适合计算机求解。文中给出了计算机求解程序。

A large quantity of computation is unavoidable in finding the solution of a con- gruence system of first degree by using congruence theorem due to repeated division algo- rithm and continued multiplication.A new method,successive approach method ,is presented in this paper,by which a proper integer is selected to fit the first and second formula,then integer satisfying the first i formulae is derived,…,the solution of the congruence system will be obtained finally.Most of computative work is cut down using this method,and the computation process is extendible,which makes the solution by computer convenient.A com- puter program is given.