CMO 2015 Problem 5

Let $p$ be a prime number for which $\frac{p-1}{2}$ is also prime, and let a, $b, c$ be integers not divisible by $p$. Prove that there are at most $1+\sqrt{2 p}$ positive integers $n$ such that $n<p$ and $p$ divides $a^{n}+b^{n}+c^{n}$.