olymmath

ISL 2021 N5

    Prove that there are only finitely many quadruples (a,b,c,n)(a, b, c, n) of positive integers such that n!=an−1+bn−1+cn−1.n!=a^{n-1}+b^{n-1}+c^{n-1} .

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

    Official text: IMO 2021 Shortlist booklet, page 10.

    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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