PL-OM 2011 Problem 4

Determine all pairs of functions $f,g:\mathbb{R}\rightarrow\mathbb{R}$ such that for any $x,y\in \mathbb{R}$ , $f(x)f(y)=g(x)g(y)+g(x)+g(y).$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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