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

1. ## 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

2. Originally Posted by joshquick
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 $1\leqslant \text{LHS}\leqslant 3$.