Let $a > 2$ be a natural number. Show that there are infinitely many natural numbers n such that $a^n \equiv -1$ (mod $n^2$).
Source: Indian Postal Coaching 2009 set 2 p2
Tags: number theory, remainder
Let $a > 2$ be a natural number. Show that there are infinitely many natural numbers n such that $a^n \equiv -1$ (mod $n^2$).