Prove that if n[tex]\equiv3[/tex] (mod 4), then n cannot be represented as a sum of two squares.
If you prefer the 'long' two-line version:"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.
It is the same, you're right. Yours might even be more understandable. I claim only that mine is shorter. :)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.