olymmath

ISL 2007 N6

    Let kk be a positive integer. Prove that the number (4k2−1)2\left(4 k^{2}-1\right)^{2} has a positive divisor of the form 8kn−18 k n-1 if and only if kk is even. (United Kingdom)

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

    Official text: IMO 2007 Shortlist booklet, page 63.

    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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