Question

For \(p>1\), integer \(p\) can only be prime iff\[\sum_{i=1}^{p-1}i^{p-1}\equiv-1\pmod p\]Prove?

Answer 1

Whoops, ahaha, fixed the TeX.

Answer 2

*

Answer 3

*

Answer 4

*

Answer 5

lol..

Answer 6

Use fermat's little theorem.

a^p = a which is equivalent to
a^(p-1) = 1

Now proceed with the summation.