MathNet 2017-part-03 — 176 problems (EN–VI) Question 69

Let $\{a_n\}$ be a sequence of integers satisfying the following condition for all positive integral values of $n$: $a_n + a_{n+1} = 2a_{n+2}a_{n+3} + 2016$. Find all possible values of $a_1$ and $a_2$.