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
![$a,f(b)$](http://latex.artofproblemsolving.com/8/e/6/8e645a0393a2bb5633d525e276321203781753af.png)
![$f(b+f(a)-1)$](http://latex.artofproblemsolving.com/7/e/2/7e24db20845eba2e50f55b74a222d4ef4858c53a.png)
(A triangle is non-degenerate if its vertices are not collinear.)
Author: Bruno Le Floch, France
--Bugi 10:30, 23 July 2009 (UTC)Bugi