MathDB

FE integers

Source: 1996 Korea National Math olympiad #2

March 22, 2018

functional equationalgebranumber theoryfunction

Problem Statement

Let the

f:\mathbb{N}\rightarrow\mathbb{N}

be the function such that (i) For all positive integers

n,

f(n+f(n))=f(n)

(ii)

f(n_o)=1

for some

n_0

Prove that

f(n)\equiv 1.