Question 10
(IND 5) A natural number $n$ is said to have the property $P$ if whenever $n$ divides $a^n-1$ for some integer $a$, $n^2$ also necessarily divides $a^n-1$.
(a) Show that every prime number has property $P$.
(b) Show that there are infinitely many composite numbers $n$ that possess property $P$.
(a) Show that every prime number has property $P$.
(b) Show that there are infinitely many composite numbers $n$ that possess property $P$.