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Prove that if n[tex]\equiv3[/tex] (mod 4), then n cannot be represented as a sum of two squares.
It may not be the prettiest proof, but I'm sure the other regulars will swoop in with a two-liner and make me look like a muppet. ;D
"Squares are zero or one mod 4."
I think that taking this statement for granted is sort of presupposing the conclusion. Although a simple proof of this would certainly prove the guy's thing.
I suppose that does work, too. Interestingly enough it is exactly what I did, except that I didn't realize that you only had to show it for 0, 1, 2, and 3. You're right, of course.