MathDB
All functions f(x-f(y))=f(x+y^n)+f(f(y)+y^n) with fixed n

Source: China TST 2011 - Quiz 2 - D1 - P1

May 20, 2011
functionalgebra unsolvedalgebra

Problem Statement

Let n≥2n\geq 2 be a given integer. Find all functions f:R→Rf:\mathbb{R}\rightarrow \mathbb{R} such that f(x−f(y))=f(x+yn)+f(f(y)+yn),∀x,y∈R.f(x-f(y))=f(x+y^n)+f(f(y)+y^n), \qquad \forall x,y \in \mathbb R.
Back to ProblemsView on AoPS