(In reply to Mod 4
by Ady TZIDON)
I'd be interested in your Mod 4 proof, since I couldn't make that work, and I have doubts that it does work.
b^2-4*a*c = 1 (mod 4), so it looks like it could conceivably be a square.
Plus, 4ac = 0 (mod 4), even if a or c are even, which is another reason I doubt it will work.
But I'd like to be proved wrong,