2007 IMO Shortlist Problems/A2

Revision as of 08:19, 3 August 2023 by Dondee123 (talk | contribs) (Created page with "== Problem == (''Bulgaria'') Consider those functions <math>f:\mathbb{N}\to\mathbb{N}</math> which satisfy the condition <cmath>f(m+n)\ge f(m)+f(f(n))−1</cmath> for all <mat...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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.)