IMO Shortlist 2011 problem A3


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23. lipnja 2013.
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Determine all pairs (f,g) of functions from the set of real numbers to itsels that satisfy g(f(x+y)) = f(x) + (2x + y)g(y) for all real numbers x and y.

Proposed by Japan
Izvor: Međunarodna matematička olimpijada, shortlist 2011