Describe the set of prime numbers that can divide integers of the form $n^2 + 1$ where $n\in\mathbb{Z}$. Then, prove that the set of primes occurring is infinite.
So far what I came up with is that by Euler’s criterion, $a^{\frac{p-1}{2}}+1\equiv0{\pmod{p}}$. I have no idea what to do next.