Since set: for some
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!
PS. Do not double post, see here