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finding a given value of a function

Source: IrMO 2022

May 8, 2022

functionalgebra

Problem Statement

4. Let

\mathbb{N}

denote the strictly positive integers. A function

f(n+1)

:

\mathbb{N}

\to

\mathbb{N}

has the following properties which hold for all

n \in

\mathbb{N}

:
a)

f(n)

<

f(n+1)

; b)

f(f(f(n)))

= 4

n

Find

f(2022)

.

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