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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 $\displaystyle n\equiv 0\text{ mod }2\implies n^{21}\equiv 0^{21}=0\equiv n\text{ mod }2$ or $\displaystyle n\equiv 1\text{ mod }2\implies n^{21}\equiv 1^{21}=1\equiv n\text{ mod }2$
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    MHF Contributor chisigma's Avatar
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    In other words...

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

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

    Kind regards

    $\displaystyle \chi$ $\displaystyle \sigma$
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