MathNet 1986 — Part 01 Question 9

Let $u_{1}, u_{2}, u_{3}, \ldots$ be a sequence of integers satisfying the recurrence relation $u_{n+2} = u_{n+1}^{2} - u_{n}$. Suppose $u_{1} = 39$ and $u_{2} = 45$. Prove that $1986$ divides infinitely many terms of the sequence.