MathNet 2013 Question 7

Let $\{a_n\}_{n\ge1}$ be a sequence of natural numbers such that $0\lt a_{n+1}-a_n\le m$ for every $n\ge1$, where $m\in\mathbb N$ is fixed. Prove that there are terms $a_r,a_s$ with $a_r\mid a_s$ and $1\le r\lt s$.