Results 1 to 3 of 3

Thread: Sum of quintuples

  1. #1
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1

    Sum of quintuples

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

    $\displaystyle \Big(\sum_{1 \leq a <b<c<d<e\leq p-1}abcde\Big) \equiv 0 \mod p$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2008
    From
    Guernsey
    Posts
    69
    $\displaystyle (x-1)(x-2)(x-3) \cdots(x-(p-1)) = x^{p-1}-1$ over $\displaystyle \mathbb{F}_p$

    Using Vieta's relations, the question asks for the coefficient of $\displaystyle x^{p-6}$ which is zero when $\displaystyle p \ge 7$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Bruno J.'s Avatar
    Joined
    Jun 2009
    From
    Canada
    Posts
    1,266
    Thanks
    1
    Awards
    1
    That's it!
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum