Question 9
Let be given a sequence of positive integers $\{a_n\}$, $n = 1, 2, 3, \ldots$, satisfying the condition
$$
0 \lt a_{n+1} - a_n \le 2001
$$
for every $n = 1, 2, 3, \ldots$. Prove that there exists an infinite number of couples of positive integers $(p, q)$ such that $p \lt q$ and $a_p$ is a divisor of $a_q$.
$$
0 \lt a_{n+1} - a_n \le 2001
$$
for every $n = 1, 2, 3, \ldots$. Prove that there exists an infinite number of couples of positive integers $(p, q)$ such that $p \lt q$ and $a_p$ is a divisor of $a_q$.