olymmath

ISL 2015 C6

    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.

    Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.

    Official text: IMO 2015 Shortlist booklet, page 6.

    Solutions

    Official solution Solution 1 by the IMO Problem Selection Committee

    The terms of the source let olymmath link to this solution but not copy it. Read the solution (IMO official site).

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