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Function with asymptotic irrational slope

Source: kjmo 2013 pr 7

September 21, 2017
Functional Equations

Problem Statement

Let f:N⟶Nf:\mathbb{N} \longrightarrow \mathbb{N} be such that for every positive integer nn, followings are satisfied. i. f(n+1)>f(n)f(n+1) > f(n) ii. f(f(n))=2n+2f(f(n)) = 2n+2 Find the value of f(2013)f(2013). (Here, N\mathbb{N} is the set of all positive integers.)
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