# Determine all functions $f : \mathbb{N} \rightarrow \mathbb{N}$ such that, for every positive integer $n$, we have: $2n+2001≤f(f(n))+f(n)≤2n+2002$.

Determine all functions $$f : \mathbb{N} \rightarrow \mathbb{N}$$ such that, for every positive integer $$n$$, we have: $$2n+2001≤f(f(n))+f(n)≤2n+2002\,.$$

I don't know where to start as in is there a function that I can get to the solution by slightly modifying it? Any ideas

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• Please credit the original source. – Apass.Jack Nov 26 '18 at 3:59