## Numbers 561 and 1105

The two smallest composite numbers for which   $n|(2^n - 2)$   and   $n|(3^n - n)$ are   $561$   and   $1105$.

N.B.   It is not known whether there exist infinitely many composite numbers for which   $n|(2^n - 2)$   and   $n|(3^n - n)$