MathDB
injectivity in 0

Source: Romanian District Olympiad, grade 10, p4

March 10, 2024
algebrafunctional equation

Problem Statement

Let n∈N∖{0}n\in\mathbb{N}\setminus\left\{0\right\} be a positive integer. Find all the functions f:R→Rf:\mathbb{R}\rightarrow \mathbb{R} satisfying that : f(x+y2n)=f(f(x))+y2n−1f(y),(∀)x,y∈R,f(x+y^{2n})=f(f(x))+y^{2n-1}f(y),(\forall)x,y\in\mathbb{R}, and f(x)=0f(x)=0 has an unique solution.
Back to ProblemsView on AoPS