CMO 1986 Problem 5

Let $u_1$ , $u_2$ , $u_3$ , $\dots$ 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.