IMO 2011 Shortlist C4

Determine the greatest positive integer k that satisfies the following property: The set of positive integers can be par...

IMO 2011 Shortlist C4

Category: Combinatorics

Problem

Determine the greatest positive integer k that satisfies the following property: The set of positive integers can be partitioned into k subsets A1,A2,...,Ak such that for all integers n ≥ 15 and all i ∈ {1,2,...,k} there exist two distinct elements of Ai whose sum is n.