I need to proove that if n=7(mod 8 ), then n does not equal x^2+y^2+z^2, for any x,y,z, integers. (the first equals sign is supposed the be a modulo symbol)
I've reduced the problem to finding that n=8s+7, for any s, but how do I prove that this does not equal the second statement above, or am i going in the right direction?