Using Fermat's Little Theorem, prove $1^{p-1} + 2^{p-1} + 3^{p-1} +\ldots+(p-1)^{p-1} \equiv -1 \pmod p$
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$