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Math Help - [SOLVED] Prime number proof

  1. #1
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    [SOLVED] Prime number proof

    I wasn't sure where to put this, but here goes.

    \frac{n^x - n}{x} is a formula we have been given.
    We have been told that the denominator is a factor when x is prime and we're expected to prove/show that to be the truth.

    It works experimentally (substituting numbers) but I can't actually find a proper proof.

    Best I could come up with is:

    Let it equal \frac{a}{b} so that therefore b is a factor of a (a=by, y is an integer)

     n^x - n = a = by
    and
    x = b

    That leads me to subsitute them back and get:

    \frac{by}{b}

    which simplifies to give y, which is an integer.

    Any proper proofs?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Russ View Post
    I wasn't sure where to put this, but here goes.

    \frac{n^x - n}{x} is a formula we have been given.
    We have been told that the denominator is a factor when x is prime and we're expected to prove/show that to be the truth.

    It works experimentally (substituting numbers) but I can't actually find a proper proof.

    Best I could come up with is:

    Let it equal \frac{a}{b} so that therefore b is a factor of a (a=by, y is an integer)

     n^x - n = a = by
    and
    x = b

    That leads me to subsitute them back and get:

    \frac{by}{b}

    which simplifies to give y, which is an integer.

    Any proper proofs?
    The numerator factors as follows

    n(n^{x-1}-1)

    If x is prime then by fermat little theorem  x | n^{x-1}-1

    Fermat's little theorem - Wikipedia, the free encyclopedia
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  3. #3
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    Thanks. Didn't know about that theorem, was trying to do it with logic.
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