olymmath

ISL 2009 A7

  • Answer

Find all functions ff from the set of real numbers into the set of real numbers which satisfy for all real x,yx, y the identity f(xf(x+y))=f(yf(x))+x2f(x f(x+y))=f(y f(x))+x^{2}

Dataset text NuminaMath olympiads. Quoted with source.

Official text: IMO 2009 Shortlist booklet, page 7.

Show the answer

f(x) = \eta x

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

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