Problem

Source: Kosovo MO 2010 Grade 12, Problem 4

Tags: number theory



Let $(p_1,p_2,..., p_n)$ be a random permutation of the set $\{1,2,...,n)$. If $n$ is odd, prove that the product $(p_1-1)\cdot (p_2-2)\cdot ...\cdot (p_n-n)$ is an even number. @below fixed.