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在一千多年前的《孙子算经》中就有记载余数研究,称之为“孙子定理”或“中国剩余定理”。现在人们已经非常熟悉一些十进制中的整除和同余规律。但是,这些计算余数的方法都是对单个除数描述的,我们猜想,有没有通用的求余数规律,或者对某一类除数(特别是某些质数)存在一定通用求余数规律呢?如果存在,就可以简化一些除数为质数的求余算法,方便程序统一实现。
More than a thousand years ago, “Sun Tzuosoji” there is a recorded remainder study, called “grandchildren theorem” or “China's residual theorem.” Nowadays people are already very familiar with the rules of divisions and congruence in some decimals. However, these methods of calculating the remainder are all described in terms of a single divisor. Suppose we have a general rule of law for the remainder of the remainder, or the existence of a generalized law of remainder for a class of divisors (especially some prime numbers)? If so, You can simplify some of the remainder of the division algorithm for the primes, to facilitate the realization of a unified program.