PL-OM 1988 Problem 5

The sequence $a_1, a_2, a_3, ...$ is defined by $a_1 = a_2 = a_3 = 1$ , $a_{n+3} = a_{n+2}a_{n+1} + a_n$ . Show that for any positive integer $r$ we can find $s$ such that $a_s$ is a multiple of $r$ .