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

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

    Quote 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.
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