Suppose that $n$ is a composite, squarefree integer such that for every prime divisor $p$ of $n$, we have $(p - 1) | (n - 1)$. Prove that $n$ is a Carmichael number.
Having a lot of trouble with this problem, looking through my notes couldn't really find anything useful apart from the definition of a Carmichael number. After going back to my professor his two hints were to use Fermat's Little Theorem and to consider what the prime factorization of n looks like. This wasn't much help, and any further assistance is greatly appreciated.
