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Thread: Factorial proof

  1. #1
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    Factorial proof

    Hi all
    I've got a feeling this is a really simple question but I can't see it.

    Explain why p divides (2p-1)!

    Thanks, Alex
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  2. #2
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    Re: Factorial proof

    Quote Originally Posted by alexlbrown59 View Post
    Hi all
    I've got a feeling this is a really simple question but I can't see it.

    Explain why p divides (2p-1)!

    Thanks, Alex
    $(2p-1)! = (2p-1)(2p-2)\dots (p+1)(p)(p-1)\dots (2)$

    $2p-1>p,~\forall p>1$

    so $p$ will appear as a product term in this factorial for $p>1$

    $1$ divides everything so it works for $p=1$ as well
    Thanks from topsquark
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