7
We say an integer $M>1$ is good if whenever $n^n \equiv 1 \mod M$ then we also have $n \equiv 1 \mod M$ and $bad$ otherwise, for any integer $n\ge 2$ . Prove that all odd $M$ are bad. Find all good $M$ .
My progress: First taking example, we get Among $M \in \{2,3,4,5\}$ $ , 2,4$ are $good$...