olymmath

ISL 2018 N3

    Define the sequence a0,a1,a2,…a_{0}, a_{1}, a_{2}, \ldots by an=2n+2⌊n/2⌋a_{n}=2^{n}+2^{\lfloor n / 2\rfloor}. Prove that there are infinitely many terms of the sequence which can be expressed as a sum of (two or more) distinct terms of the sequence, as well as infinitely many of those which cannot be expressed in such a way. (Serbia)

    Dataset text NuminaMath olympiads. Quoted with source.

    Official text: IMO 2018 Shortlist booklet, page 9.

    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).

    Locator isl/2018/n3 · Tag YGHCF9JSSC · Edit this page on GitHub · Keys: j next, k previous