IMO 2015 Shortlist C6
Let S be a nonempty set of positive integers. We say that a positive integer n is clean if it has a unique representatio...
Category: Combinatorics
Problem
Let S be a nonempty set of positive integers. We say that a positive integer n is clean if it has a unique representation as a sum of an odd number of distinct elements from S. Prove that there exist infinitely many positive integers that are not clean. (U.S.A.)