Find all functions such that for all real numbers and .
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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 $y$.
Source: Međunarodna matematička olimpijada, shortlist 2005
Školjka 
such that 
for all real numbers 
and 
.