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Math Help - Fermat's Little Theorem

  1. #1
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    Fermat's Little Theorem

    Prove that 12\ |\ n^2-1 if g.c.d. (n,6) = 1.
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    MHF Contributor chisigma's Avatar
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    If g.c.d. (n,6) = 1 that means that 2 \nmid n and 3 \nmid n, i.e. n is and odd number non multiple of 3. But if 2 \nmid n and 3 \nmid n means also that n-1 and n+1 are both even numbers and 3 devides one of them. The conclusion is that...

    2\cdot 2\cdot 3 \mid (n+1)\cdot (n-1)

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    \chi \sigma
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  3. #3
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    Quote Originally Posted by chisigma View Post
    If g.c.d. (n,6) = 1 that means that 2 \nmid n and 3 \nmid n,


    i.e. n is and odd number non multiple of 3. But if 2 \nmid n and 3 \nmid n means also that n-1 and n+1 are both even numbers and 3 devides one of them. The conclusion is that...

    2\cdot 2\cdot 3 \mid (n+1)\cdot (n-1)

    Kind regards

    \chi \sigma
    .
    Follow Math Help Forum on Facebook and Google+

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