IMO 2007 Shortlist A2

Consider those functions f : N → N which satisfy the condition f(m + n) ≥ f(m) + f f(n)  − 1 (1) for all m,n ∈ N. Find ...

IMO 2007 Shortlist A2

Category: Algebra

Problem

Consider those functions f : N → N which satisfy the condition f(m + n) ≥ f(m) + f f(n)  − 1 (1) for all m,n ∈ N. Find all possible values of f(2007). (N denotes the set of all positive integers.) (Bulgaria)