MathDB
Macedonia National Olympiad 2017 Problem 1

Source: Macedonia National Olympiad 2017

April 8, 2017
functionalgebra

Problem Statement

Find all functions f:N→Nf:\mathbb{N} \to \mathbb{N} such that for each natural integer n>1n>1 and for all x,y∈Nx,y \in \mathbb{N} the following holds:
f(x+y)=f(x)+f(y)+∑k=1n−1(nk)xn−kykf(x+y) = f(x) + f(y) + \sum_{k=1}^{n-1} \binom{n}{k}x^{n-k}y^k
Back to ProblemsView on AoPS