2009 IMO Problems/Problem 5

Problem

Determine all functions from the set of positive integers to the set of positive integers such that, for all positive integers and , there exists a non-degenerate triangle with sides of lengths

and .

(A triangle is non-degenerate if its vertices are not collinear.)

Author: Bruno Le Floch, France

--Bugi 10:30, 23 July 2009 (UTC)Bugi