IMO Shortlist 2005 problem A4


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2. travnja 2012.
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Find all functions f: \mathbb{R}\to\mathbb{R} such that f\left(x+y\right)+f\left(x\right)f\left(y\right)=f\left(xy\right)+2xy+1 for all real numbers x and y.
Izvor: Međunarodna matematička olimpijada, shortlist 2005