MathDB

Easy Functional Equation

Source: 2021 Taiwan TST Round 2 Mock Day 2 P5

April 10, 2021

algebrafunctional equationarrowsTaiwan

Problem Statement

Let

\|x\|_*=(|x|+|x-1|-1)/2

. Find all

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

such that f^{(\|f(x)-x\|_*)}(x)=x, \forall x\in\mathbb{N}. Here

f^{(0)}(x)=x

and

f^{(n)}(x)=f(f^{(n-1)}(x))

for all

n\in\mathbb{N}

.
Proposed by usjl