4

Part of 2017 Singapore Senior Math Olympiad

Problems(1)

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

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

Find all functions

f : Z^+ \to Z^+

f(k + 1) >f(f(k))

k > 1

Z^+

is the set of positive integers.

inequalitiesFunctional inequalityfunctionalalgebra