IMO 2011 Shortlist C4
Determine the greatest positive integer k that satisfies the following property: The set of positive integers can be par...
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.