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Math Help - congruence question

  1. #1
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    congruence question

    Prove that the congruence
    (x^2 - 2)(x^2 - 17)(x^2 - 34) = 0 (mod p)
    has a solution for every prime p.

    No idea how to do this, can anyone help?
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by johndoe3344 View Post
    Prove that the congruence
    (x^2 - 2)(x^2 - 17)(x^2 - 34) = 0 (mod p)
    has a solution for every prime p.

    No idea how to do this, can anyone help?
    If  \left(\frac2p\right)=1 or  \left(\frac{17}{p}\right)=1 then we're done.

    Otherwise  \left(\frac{34}{p}\right)=\left(\frac2p\right)\lef  t(\frac{17}{p}\right) = (-1)(-1) = 1
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