International Mathematical Olympiad 1975 Problem 2

Let $a_1, a_2, a_3, \cdots$ be an infinite increasing sequence of positive integers. Prove that for every $p \geq 1$ there are infinitely many $a_m$ which can be written in the form

$$a_m = xa_p + ya_q$$

with $x, y$ positive integers and $q > p$.