Find $\displaystyle r \in Z$ such that $\displaystyle 0 \leq r \leq 4096$ and $\displaystyle 2^{4096} \equiv r \,(mod \,4097)$ Why does this prove that $\displaystyle 4097$ is not a prime? According to FLT r would be 1 if 4097 where a prime, but now it isn't, so, help appreciated.