olymmath

ISL 2011 A3

    Determine all pairs (f,g)(f, g) of functions from the set of real numbers to itself that satisfy g(f(x+y))=f(x)+(2x+y)g(y)g(f(x+y))=f(x)+(2 x+y) g(y) for all real numbers xx and yy.

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

    Official text: IMO 2011 Shortlist booklet, page 5.

    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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