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f(m + n) >= f(m) + f(f(n)) - 1

Source: IMO Shortlist 2007, A2, AIMO 2008, TST 2, P1, Ukrainian TST 2008 Problem 8

July 13, 2008
algebraFunctional inequalityIMO Shortlist

Problem Statement

Consider those functions f:N↦N f: \mathbb{N} \mapsto \mathbb{N} which satisfy the condition f(m \plus{} n) \geq f(m) \plus{} f(f(n)) \minus{} 1 for all m,n∈N. m,n \in \mathbb{N}. Find all possible values of f(2007). f(2007).
Author: Nikolai Nikolov, Bulgaria
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