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当我們想知道一个整數能不能除尽另一个整數時,一般地,除了是用2,3,5,…这些極个別的數去除別的數之外,總得老老实实去除一除,这件工作是很麻煩的,这裹介紹一种方法,利用它能判別一个數能不能除尽另一个數。在我們只需要知道一个數能不能除尽另一数而不用知道它們的商時,这个方法是很適用的。为了說着方便,当然可以假定除數D和被除數N都是正的。我們知道,被除數N越小,除起來就越省力;要是我們对於D和N能找到一个比N小的R,使得D|R是D|N的充分必要条件,那問題不是就简單了嗎?这里介紹的方法的基本意思,就是給出一个規律,使我們对任意的正整數D,N,都能找到一个比N小的R,滿足: D|R(?)D|N
When we want to know if an integer can’t divide another integer, generally, except that we use 2, 3, 5,... to remove other numbers, we have to remove a division. The work is very troublesome. This package introduces a method that can be used to determine if a number can not be used to divide another number. This method works well when we only need to know that one number can’t divide another number without knowing their quotient. For convenience, it can be assumed that both the divisor D and the dividend N are positive. We know that the smaller the dividend N is, the harder it is to remove it; if we can find an R smaller than N for D and N, making D|R a necessary and sufficient condition for D|N, then the problem is not simple. The basic idea of the method described here is to give a rule that we can find an R smaller than N for any positive integer D, N, satisfying: D|R(?)D|N