2007 IMO Shortlist Problems/A2

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Problem

(Bulgaria) Consider those functions $f:\mathbb{N}\to\mathbb{N}$ which satisfy the condition

\[f(m+n)\ge f(m)+f(f(n))−1\] (Error compiling LaTeX. Unknown error_msg)

for all $m$, $n$\in\mathbb{N}$. Find all possible values of$f(2007)$. ($\mathbb{N}$ denotes the set of all positive integers.)