Past exam of the mathematics course of the University of Cambridge / 2005 / ii / Paper 4 / 1H / Solution

An odd composite integer $n>1$ coprime to $b$ is a Fermat pseudoprime to base $b$ if $b^{n-1}\equiv 1(\mathrm{mod}n)$. A Carmichael number is a composite integer satisfying this congruence for every integer $b$ coprime to $n$. The Korselt criterion says that a composite $n$ is a Carmichael number exactly when it is squarefree and $p-1$ divides $n-1$ for every prime divisor $p$ of $n$.