VN-TST 2001 Problem 6

Let a sequence $\{a_n\}$, $n \in \mathbb{N}^{*}$ given, satisfying the condition

$$0 < a_{n+1} - a_n \leq 2001$$

for all $n \in \mathbb{N}^{*}$

Show that there are infinitely many pairs of positive integers $(p, q)$ such that $p < q$ and $a_p$ is divisor of $a_q$.