Only integers congruent to 0 or 1(mod 4) are possible.
If b is even b^2 is a multiple of 4 so b^2-4ac is a multiple of 4
If b is odd, then b=2k+1 so b^2 is 4k^2 + 4k + 1 which is congruent to 1(mod4) and so b^2-4ac is too.
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