"Let p be a prime such that there exists a solution to the congruence [tex]x^2\equiv - 2\mod p[/tex]. THEN there are integers a and b such that [tex]a^2 + 2b^2 = p[/tex] or [tex]a^2 + 2b^2 = 2p[/tex]." ============================ I don't see why this is true. How can we prove this using basic concepts? We know that there exists some integer x such that p|(x2 -2), what's next? Any help is appreciated!