IMO Shortlist 1999 problem A5

Find all the functions $f: \mathbb{R} \mapsto \mathbb{R}$ such that

$f(x-f(y))=f(f(y))+xf(y)+f(x)-1$

for all $x,y \in \mathbb{R}$ .

Izvor: Međunarodna matematička olimpijada, shortlist 1999

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