Let $n$ be a positive integer, and let $p$ be a prime number. Prove that if $p^p | n!$, then $p^{p+1} | n!$.
Problem
Source: MOP 2006 Homework - Black Group
Tags: factorial, number theory unsolved, number theory
Source: MOP 2006 Homework - Black Group
Tags: factorial, number theory unsolved, number theory
Let $n$ be a positive integer, and let $p$ be a prime number. Prove that if $p^p | n!$, then $p^{p+1} | n!$.