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f(k + 1) >f(f(k)) for k > 1 when f : Z^+ \to Z^+

Source: Singapore Senior Math Olympiad 2017 2nd Round p4 SMO

March 26, 2020
inequalitiesFunctional inequalityfunctionalalgebra

Problem Statement

Find all functions f:Z+ā†’Z+f : Z^+ \to Z^+ such that f(k+1)>f(f(k))f(k + 1) >f(f(k)) for k>1k > 1, where Z+Z^+ is the set of positive integers.
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