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Math Help - Is there a prime p for which the equation does not hold

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    Is there a prime p for which the equation does not hold

    the following does not hold?

    a^{10} + b^{10} + c^{10} = 11d^2 \text{ mod } p

    I tried p = 3 and p = 11, and I couldn't get anywhere, since I can still have trivial solutions.

    Thanks!
    -- Josh
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by joshquick View Post
    the following does not hold?

    a^{10} + b^{10} + c^{10} = 11d^2 \text{ mod } p

    I tried p = 3 and p = 11, and I couldn't get anywhere, since I can still have trivial solutions.

    Thanks!
    -- Josh
    What's your question? Are you looking for a prime for which the above equation doesn't have a non-trivial solution? Then p=11 works since assuming (a,b,c)\ne (11,11,11) then the RHS is zero but 1\leqslant \text{LHS}\leqslant 3.
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