MathDB

11.8

Part of 1998 All-Russian Olympiad Regional Round

Problems(1)

Tricky combo, and the need to eliminate m.

Source: Russia 1998

10/5/2017
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.
Combinatorial Number Theorycombinatoricsalgebrainequalitiesnumber theory