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Math Help - Fermat's Little Theorem

  1. #1
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    Fermat's Little Theorem

    Show that
    (p-1)(p-2)...(p-r)==(-1)^r*r!(mod p)
    for r=1, 2, ..., p-1.

    I am totally lost on this one... Can you help me get started? Thanks.

    Oops, this should have said Wilson's theorem in the title.
    Last edited by tarheelborn; February 24th 2010 at 08:16 AM. Reason: Wrong theorem in title
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  2. #2
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    Remember this is all mod p.
    So
    1 = p+1 = 2*p+1, etc.

    In particular,
    p-1 = -1
    p-2 = -2, etc.

    Try replacing each term on the left with 'something equal to it mod p' on the right.
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  3. #3
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    So something like
    -1 * -2 * ... * -r == (-1)(-2)...(-r)(mod p)
    == (-1)^r(1*28...*r)(mod p)
    == (-1)^r * r! (mod p)
    and we are done, right?

    Thank you.
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