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fe with natural on reals

Source: Baltic Way 2021, Problem 1

November 15, 2021
algebraalgebra proposedfunctional equation

Problem Statement

Let nn be a positive integer. Find all functions f ⁣:R→Rf\colon \mathbb{R}\rightarrow \mathbb{R} that satisfy the equation (f(x))nf(x+y)=(f(x))n+1+xnf(y) (f(x))^n f(x+y) = (f(x))^{n+1} + x^n f(y) for all x,y∈Rx ,y \in \mathbb{R}.
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