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Part of 2018 Spain Mathematical Olympiad

Problems(1)

f(x+f(y))=yf(xy+1)

Source:

Find all functions such that f: \mathbb{R}^\plus{} \rightarrow \mathbb{R}^\plus{} and f(x\plus{}f(y))\equal{}yf(xy\plus{}1) for every x,y\in \mathbb{R}^\plus{}.

functionalgebra unsolvedalgebra