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Find all functions f:N--> N

Source: Saudi Arabia IMO TST Day I Problem 4

July 22, 2014
functioninductionalgebra unsolvedalgebra

Problem Statement

Find all functions f:N→Nf:\mathbb{N}\rightarrow\mathbb{N} such that f(n+1)>f(n)+f(f(n))2f(n+1)>\frac{f(n)+f(f(n))}{2} for all n∈Nn\in\mathbb{N}, where N\mathbb{N} is the set of strictly positive integers.
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