整数除法属性 [英] integer division properties

问题描述

以下整数算术属性是否成立？

does the following integer arithmetic property hold?

(m/n)/l == m/(n*l)

起初，我以为我知道答案（不成立），但现在不确定。
它适用于所有数字还是仅适用于某些条件，即 n> l ？

At first I thought I knew answer (does not hold), but now am not sure. Does it hold for all numbers or only for certain conditions, i.e. n > l?

该问题与计算机算术有关，即 q = n / m，q * m！= n ，忽略溢出。

the question pertains to computer arithmetic, namely q = n/m, q*m != n, ignoring overflow.

推荐答案

Case1 assume m = kn+b (b<n),
left = (m/n)/l = ((kn+b)/n)/l = (k+b/n)/l = k/l (b/n=0, because b<n)
right = (kn+b)/(n*l) = k/l + b/(n*l) = k/l (b/(n*l)=0, because b<n)
=> left = right

Case2 assume m = kn,
left = (m/n)/l = (kn/n)/l = k/l
right = kn/(n*l) = k/l
=> left = right

So, (m/n)/l == m/(n*l)

这篇关于整数除法属性的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！