Difference between revisions of "2007 IMO Shortlist Problems/A2"

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== Problem ==
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(''Bulgaria'')
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Consider those functions <math>f:\mathbb{N}\to\mathbb{N}</math> which satisfy the condition
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<center><math>f(m+n)\ge f(m)+f(f(n))-1</math></center>
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for all <math>m, n\in\mathbb{N}</math>. Find all possible values of <math>f(2007).</math>
  
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(<math>\mathbb{N}</math> denotes the set of all integers.)

Revision as of 07:30, 3 August 2023

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.)