MathDB
not all sufficiently large integers are clean

Source: 2015 IMO Shortlist C6, Original 2015 IMO #6

July 7, 2016
IMO ShortlistcombinatoricsAdditive combinatorics

Problem Statement

Let SS be a nonempty set of positive integers. We say that a positive integer nn is clean if it has a unique representation as a sum of an odd number of distinct elements from SS. Prove that there exist infinitely many positive integers that are not clean.
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