MathDB
IMO Shortlist 2009 - Problem A7

Source:

July 5, 2010
functionalgebrafunctional equationIMO Shortlist

Problem Statement

Find all functions ff from the set of real numbers into the set of real numbers which satisfy for all xx, yy the identity f(xf(x+y))=f(yf(x))+x2 f\left(xf(x+y)\right) = f\left(yf(x)\right) +x^2
Proposed by Japan
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