The Problem is to prove that $p|1^n+...+(p-1)^n$ for $p>n+1$, $p$ is a prime.
For $n$ being odd it is pretty straight forward. For $n$ being even, I am not able to solve it, thinking some connection with orders or primitive root(the handout is on these topics) because of $n\leq p-2$
How is this question different?
This was termed a duplicate of this $1^n +2^n + \cdots +(p-1)^n \mod p =$?
I am not able to follow from the hints and want a better hint/solution for this question.
It also has an additional condition.
