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

  • 2
    $\begingroup$ further than what? $\endgroup$ – mathworker21 Apr 15 at 10:58

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