IMO Shortlist 2009 problem A7


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2. travnja 2012.
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Find all functions f from the set of real numbers into the set of real numbers which satisfy for all x, y the identity f\left(xf(x+y)\right) = f\left(yf(x)\right) +x^2

Proposed by Japan
Izvor: Međunarodna matematička olimpijada, shortlist 2009