# Math Help - Prove that n! does not divide n^n for n>2

1. ## Prove that n! does not divide n^n for n>2

Dividing both sides by n, I get that (n-1)! | n^(n-1) => (n-1) | n^(n-1) but I'm stuck as to where to go next. Any help would be appreciated.

2. ## Re: Prove that n! does not divide n^n for n>2

Originally Posted by topsquark
Have you considered an induction proof? It's fairly simple.
Yes I did consider this but it doesn't seem simple. Suppose n! doesn't divide n^n , but that (n+1)! divides (n+1)^(n+1). Then for some k, k(n+1)! = (n+1)^(n+1). I need to now get a contradiction but I can't see how.