Let $\displaystyle p \geq 7$ be a prime. Show that

$\displaystyle \Big(\sum_{1 \leq a <b<c<d<e\leq p-1}abcde\Big) \equiv 0 \mod p$

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- Jun 15th 2009, 10:27 PMBruno J.Sum of quintuples
Let $\displaystyle p \geq 7$ be a prime. Show that

$\displaystyle \Big(\sum_{1 \leq a <b<c<d<e\leq p-1}abcde\Big) \equiv 0 \mod p$ - Jun 16th 2009, 12:44 AMSimonM
$\displaystyle (x-1)(x-2)(x-3) \cdots(x-(p-1)) = x^{p-1}-1$ over $\displaystyle \mathbb{F}_p$

Using Vieta's relations, the question asks for the coefficient of $\displaystyle x^{p-6}$ which is zero when $\displaystyle p \ge 7$ - Jun 16th 2009, 07:16 AMBruno J.
That's it! (Clapping)