中国剩余定理与同余式组

The Chinese Remainder Theorem and The System of Congruence

"中国剩余定理"是初等数论中一个很重要的定理,同时在抽象代数中占有很重要的地位。最近,匡正从组合学的角度给出了两个模的情形下的"中国剩余定理"一个证明。作者利用这个方法证明了一般情形下(即k(k≥3)个模的情形)的"中国剩余定理",同时给出了一次同余式组的一种较为简捷易懂的解法。

The Chinese Remainder Theorem is an important theory in elementarynumber theory, is also important in abstract algebra. Recently, Kuangzheng gave a method from the Combinatorics to prove the Chinese Remainder Theorem under the condition of two modules. In this paper, we proved the Chinese Remainder Theorem under the condition of modules by Kuangzheng＇ s method , and gave a easily way to resolve the system of congruences.