# Help with a modular arithmetic proof

Every integer x equals 0, 1, 2, 3 or 4 modulo 5, and if $x\equiv k\pmod{5}$, then $x^2\equiv k^2\pmod{5}$. So you only need to check that $k^2\not\equiv3\pmod{5}$ for k = 0, 1, 2, 3, 4,