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  1. #1
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    proof

    Prove that 2 divides n^21-n.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by meshel88 View Post
    Prove that 2 divides n^21-n.
    We only have two cases, either n\equiv 0\text{ mod }2\implies n^{21}\equiv 0^{21}=0\equiv n\text{ mod }2 or n\equiv 1\text{ mod }2\implies n^{21}\equiv 1^{21}=1\equiv n\text{ mod }2
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    MHF Contributor chisigma's Avatar
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    In other words...

    a) for n even also n^{21} is even so that n^{21}-n is even...

    b) for n odd also n^{21} is odd so that n^{21}-n is even...

    Kind regards

    \chi \sigma
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