MathNet 2011 Question 90

Let $a_{n+1} = a_n^3 - 2a_n^2 + 2$ for all $n \ge 1$ and $a_1 = 5$. Prove that if $p \equiv 3 \pmod 4$ is a prime divisor of $a_{2011} + 1$, then $p = 3$.