Find all pairs of functions such that for all real .
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Find all pairs of functions $f, g : \mathbb R \to \mathbb R$ such that $f \left( x + g(y) \right) = x \cdot f(y) - y \cdot f(x) + g(x)$ for all real $x, y$.
Source: Međunarodna matematička olimpijada, shortlist 2000
Školjka 
such that 
for all real 
.