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Tricky combo, and the need to eliminate m.

Source: Russia 1998

October 5, 2017
Combinatorial Number Theorycombinatoricsalgebrainequalitiesnumber theory

Problem Statement

A sequence a1,a2,⋯a_1,a_2,\cdots of positive integers contains each positive integer exactly once. Moreover for every pair of distinct positive integer mm and nn, 11998<∣an−am∣∣n−m∣<1998\frac{1}{1998} < \frac{|a_n- a_m|}{|n-m|} < 1998, show that ∣an−n∣<2000000|a_n - n | <2000000 for all nn.
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