Question

数学题如果m.n为正整数,且(y-x)的n次方分之（x-y)的m次方等于x-y,那么m.n的值为多少?

Answer 1

(x-y)^m/(y-x)^n=x-y,

(x-y)^m/[(-1)^n(x-y)^n]=x-y,

(x-y)^(m-n)=(-1)^n(x-y),

当n=2,4,6,8,...,及m-n=1,时等式成立,

所以,m=n+1,n=2,4,6,8,...