Since set: for some

So:

By Fermat's Little Theorem:

At this point assume by absurd that -2 is not a quadratic residue mod p, thus we must have (by Euclid's Lemma):

Then: so the RHS is a quadratic residue, thus by Euler's Criterion:

However: ( since 4 divides p+3, but 8 doesn't)CONTRADICTION!Do not double post, see here

PS.