olymmath

ISL 2019 A1

    Let Z\mathbb{Z} be the set of integers. Determine all functions f:Z→Zf: \mathbb{Z} \rightarrow \mathbb{Z} such that, for all integers aa and bb, f(2a)+2f(b)=f(f(a+b))f(2 a)+2 f(b)=f(f(a+b)) (South Africa)

    Dataset text NuminaMath olympiads. Quoted with source.

    Official text: IMO 2019 Shortlist booklet, page 6.

    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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