Hello, as part of a proof I am working on, I need to find all $\displaystyle p$ s.t. $\displaystyle p| 3^n + 5^n$ and $\displaystyle p | n^2 -1$. $\displaystyle n\in\mathbb{Z^{+}}$ and $\displaystyle p$ is prime. This part of my proof has stumped me and I have had no success in attacking this part and I am not sure as to whether I am just going down a blind alley here and there is more efficient way. Any help/ ideas/ hints would be much appreciated.