MathDB

Number of fixed points of certain condition functions

Source: American Mathematical Monthly

October 1, 2019

functionalgebra

Problem Statement

Let be three positive integers

a,b,c

and a function

f:\mathbb{N}\longrightarrow\mathbb{N}

defined as

f(n)=\left\{ \begin{matrix} n-a, & n>c\\ f\left( f(n+b) \right) ,& n\le c \end{matrix} \right. .

Determine the number of fixed points this function has.