推广的孙子定理

Generalized Chinese remainder theorem

孙子定理在模两两互质的条件下,给出了一次同余式组解的表达式.文献[1-2]给出模不两两互质的一次同余式组解的表达式,但计算较为复杂.利用算术基本定理,把模不两两互质的同余式组化为模两两互质的同余式组,再用孙子定理直接求解,计算相对简单一些.

When the moduli are pairwise coprime,the Chinese remainder theorem gave the explicit solution to the systems of congruences.When the moduli are not pairwise coprime,the refferences[1-2]gave the explicit solution.However,the calculation is rather complicated.Gave an easier calculation which take the fundamental theorem of arithematic to transform the moduli into coprime ones and then apply the Chinese remainder theorem.