# $N^2=2M^4-2p^2e^4$ has no integer solution

If $\gcd(M,e)=\gcd(N,e)=1$ and $p$ is prime and $p‎\equiv 5 \mod(16)$ then how I can show that $N^2=2M^4-2p^2e^4$ has no integer solution.

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You're clearly meant to consider the equation modulo $16$. Looking at it modulo $2$ is often a good way to start doing so. – Hurkyl Jan 10 '13 at 9:55

Write $N = 2n$ and divide through by $2$. Write the right hand side as a product, and show that one of the factors is a square, the other one twice a square. Reduce the equation involving twice the square mod $p$.