olymmath

ISL 2007 N3

    Let XX be a set of 10000 integers, none of them is divisible by 47 . Prove that there exists a 2007-element subset YY of XX such that a−b+c−d+ea-b+c-d+e is not divisible by 47 for any a,b,c,d,e∈Ya, b, c, d, e \in Y. (Netherlands)

    Dataset text NuminaMath olympiads. Quoted with source.

    Official text: IMO 2007 Shortlist booklet, page 58.

    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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