I had a question asking when is 3 a seventh power modulo a prime $p$ if $p=1(7)$. However, I tried to find just one example using mathematica but I went up to primes in the thousands and I still couldn't find an example, so I began thinking this was a trick question.
We were learning about quadratic reciprocity, but I wasn't sure how to extend what we learned about quadratic powers to seventh powers.