IMO 2015 Shortlist C5
Consider an infinite sequence a1,a2,... of positive integers with ai ď 2015 for all i ě 1. Suppose that for any two dist...
Category: Combinatorics
Problem
Consider an infinite sequence a1,a2,... of positive integers with ai ď 2015 for all i ě 1.
Suppose that for any two distinct indices i and j we have i ai ‰ j aj.
Prove that there exist two positive integers b and N such that
ˇ
ˇ
ˇ
ˇ
ˇ
n ÿ
i“m`1
pai ´ bq
ˇ
ˇ
ˇ
ˇ
ˇ
ď 10072
whenever n ą m ě N.
(Australia)