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f(f(n)) <= 1/2 (f(n) + n)

Source: Switzerland - 2009 Swiss MO Final Round p9

December 26, 2022
inequalitiesFunctional inequalityfunctionalalgebra

Problem Statement

Find all injective functions f:N→Nf : N\to N such that holds for all natural numbers nn: f(f(n))≤f(n)+n2f(f(n)) \le \frac{f(n) + n}{2}
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