Recent examination strategy big problems, the problem of violence hit the upright die solution, the positive solution of the problem would like to make a violent left.
Divergent thinking is not enough, brush some odd questions.
math
If it is to find the law a water problem.
Lemma: If n, m coprime, the $ k * n% m (1 <= k <= m) $ runs over 0 ~ m-1 for all values.
prove:
若存在$n*x%m==n*y%m$(x>y&&1<=x,y<=m)
则 $(x-y)*n=i*m,(x-y)*n/m=i$
Because i is an integer, m and n are coprime, the $ m \ mid (xy) $ intended to match with the title.
Then ask this question a GCD, then fine.