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Math Help - Sum of quintuples

  1. #1
    MHF Contributor Bruno J.'s Avatar
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    Sum of quintuples

    Let p \geq 7 be a prime. Show that

    \Big(\sum_{1 \leq a <b<c<d<e\leq p-1}abcde\Big) \equiv 0 \mod p
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  2. #2
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    (x-1)(x-2)(x-3) \cdots(x-(p-1)) = x^{p-1}-1 over \mathbb{F}_p

    Using Vieta's relations, the question asks for the coefficient of x^{p-6} which is zero when p \ge 7
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    That's it!
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