How to show that the square of an integer$\equiv 0,1,-1\pmod 5$ ?
I know that every integer can be expressed as $3k$, $3k+1$, $3k+2$. I tried to solve this by squaring these expressions, but I am stuck. Previously I had solved another problem like this. There I was able to show that the square of an odd integer when divided by 8, leaves remainder 1.