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Non-Standard Functional Equation ft. Real Number c

Source: Turkey Olympic Revenge 2023 P1

March 6, 2023
functional equationfunctionfunction in Rolympic revengealgebra

Problem Statement

Find all c∈Rc\in \mathbb{R} such that there exists a function f:R→Rf:\mathbb{R}\to \mathbb{R} satisfying (f(x)+1)(f(y)+1)=f(x+y)+f(xy+c)(f(x)+1)(f(y)+1)=f(x+y)+f(xy+c) for all x,y∈Rx,y\in \mathbb{R}.
Proposed by Kaan Bilge
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