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All functions with f(x)f(y)=g(x)g(y)+g(x)+g(y)

Source: LXII Polish Olympiad 2011, Problem 4

May 24, 2011
functionquadraticsalgebra unsolvedalgebra

Problem Statement

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