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2007 IMO Shortlist Problems/A2

Problem

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

$f(m+n)\ge f(m)+f(f(n))-1$

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

($\mathbb{N}$ denotes the set of all integers.)

Solution

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