Question 180
Let $p$, $q$ be given primes and the sequence $(p_{n})_{n \geq 1}$ defined recursively as follows: $p_{1} = p$; $p_{2} = q$ and $p_{n+2}$ is the largest prime divisor of the number $(p_{n} + p_{n+1} + 2016)$ for all $n \geq 1$. Prove that this sequence is bounded, that is there exists a positive real number $M$ such that $p_{n} \lt M$ for all positive integers $n$.