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Math Help - Another congruence proof

  1. #1
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    Another congruence proof

    Let p be a prime such that p >= 5. Show that 6 * (p-4)! -1 = 0 (mod p)

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  2. #2
    MHF Contributor chiph588@'s Avatar
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    By Wilson's Theorem  (p-1)!\equiv-1 \bmod{p}

    Now notice that  p-1\equiv-1,\; p-2\equiv-2,\; p-3\equiv-3 \bmod{p} .

    So  -1\equiv(p-1)! = (p-1)(p-2)(p-3)(p-4)! \equiv (-1)(-2)(-3)(p-4)! \bmod{p}

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  3. #3
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    Yes!

    Thank you so much. That was genius.
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