MathDB

x+f(y)|f(y+f(x)) and f(x)-2017|x-2017

Source: IMOC 2017 A2

August 12, 2021

algebranumber theoryfefunctional equation

Problem Statement

Find all functions

f:\mathbb N\to\mathbb N

such that \begin{align*} x+f(y)&\mid f(y+f(x))\\ f(x)-2017&\mid x-2017\end{align*}