# Thread: Help with a modular arithmetic proof

1. ## Help with a modular arithmetic proof

Show that there is no solution of "x2 is congruent to 3 modulo 5".
This is part of a piece of coursework I have for my Mathematical Foundations module but the lecturer barely covered modular arithmetic and i'm pretty terrible at proofs, so any help would be greatly appreciated, thanks.

2. ## Re: 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,