prove that the number of permutations such that the order of each element is a multiple of $d$ is $\frac{n!}{(\frac{n}{d})!d^{\frac{n}{d}}} \prod_{i=0}^{\frac{n}{d}-1} (id+1)$. proposed by Mohammad Mansouri
Problem
Source: Iran 3rd round 2011-combinatorics exam-p2
Tags: combinatorics proposed, combinatorics