Question 112
Find all positive integers $n$ satisfying both of the following conditions:
(a) the number of positive divisors of $n$ is not a multiple of 8;
(b) for every integer $x$,
$$
x^n \equiv x \mod n.
$$
(a) the number of positive divisors of $n$ is not a multiple of 8;
(b) for every integer $x$,
$$
x^n \equiv x \mod n.
$$