Hello,

Hmmm I don't see how to apply Fermat's little theorem here o.O

So you want to prove that there is no x such that , that is

If x=0(mod5), then x²=0(mod5)

If x=1(mod5), then x²=1(mod5)

If x=2(mod5), then x²=4(mod5)

If x=3(mod5), then x²=4(mod5)

If x=4(mod5), then x²=1(mod5)

thus it x doesn't exist.