m,n是正整数,在1,2...,2013中存在几个数可以表示成(nm-1)/(m-n)的形式?

题目

m,n是正整数,在1,2...,2013中存在几个数可以表示成(nm-1)/(m-n)的形式?
if m and n are positive integers,how many integers among 1,2,3,.,2013 can be represented by (mn-1)/(m-n)?

答案

2012个.除2以外的数均可以.当k≠2时,取m=k²-k-1,n=k-1(k=1,3,4,5,6,...2013)则(mn-1)/(m-n)=(k³-2k²)/(k²-2k)=k所以there are 2012 integers among 1,2,3,.,2013 can be represented by (mn-1)/...