The converse to Fermat's little theorem

Let $n>1$ be a positive integer such that

$$a^n\equiv a(\operatorname{mod}\ n)$$

for every integer $a$. The converse to Fermat's little theorem. Then $n$ must be a prime number. This statement is the converse formulation of Fermat's little theorem; it is solved, having been proved by Alford, Granville, and Pomerance in 1994.