olymmath

ISL 2010 N5

  • Answer

Let N\mathbb{N} be the set of all positive integers. Find all functions f:N→Nf: \mathbb{N} \rightarrow \mathbb{N} such that the number (f(m)+n)(m+f(n))(f(m)+n)(m+f(n)) is a square for all m,n∈Nm, n \in \mathbb{N}.

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

Official text: IMO 2010 Shortlist booklet, page 72.

Show the answer

f(n)=n+c

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

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