olymmath

IMO 2004 Problem 2

  • Day 1

Find all polynomials ff with real coefficients such that for all reals a,b,ca,b,c such that ab+bc+ca=0ab+bc+ca = 0 we have the following relations

f(a−b)+f(b−c)+f(c−a)=2f(a+b+c).f(a-b) + f(b-c) + f(c-a) = 2f(a+b+c).

Attachments:

logo2004.jpg

Dataset text AI-MO AoPS. Quoted with source.

Official text: IMO 2004 official English paper, page 1.

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