MathDB

Iterative F ineq on non-negative integers

Source: MEMO 2024 I1

August 26, 2024

algebraSequencesfunctionsmonotoneconstructionFunctional inequalityfunction

Problem Statement

Let

\mathbb{N}_0

denote the set of non-negative integers. Determine all non-negative integers

k

for which there exists a function

f: \mathbb{N}_0 \to \mathbb{N}_0

such that

f(2024) = k

and

f(f(n)) \leq f(n+1) - f(n)

for all non-negative integers

n