# How to approach this sequence problem on analysis

A sequence of positive integers $$a_n$$ contains each positive integer exactly once. Assume that if $$m\neq n$$ then $$\frac{1}{1998}<\frac{\vert a_m-a_n\vert}{\vert m-n\vert}<1998$$

Prove that $$\vert a_n −n\vert < 2000000$$ for all $$n$$

I tried but could't proceed further

• further than what? – mathworker21 Apr 15 at 10:58