MathDB

Finding Strictly Increasing Functions

Source: Romanian District Olympiad 2018 - Grade IX - Problem 1

March 10, 2018

function

Problem Statement

Find all strictly increasing functions

f : \mathbb{N} \to \mathbb{N}

such that

\frac {f(x) + f(y)}{1 + f(x + y)}

is a non-zero natural number, for all

x, y\in\mathbb{N}