Difference between revisions of "2007 IMO Shortlist Problems/A2"
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+ | == Problem == | ||
+ | (''Bulgaria'') | ||
+ | Consider those functions <math>f:\mathbb{N}\to\mathbb{N}</math> which satisfy the condition | ||
+ | <center><math>f(m+n)\ge f(m)+f(f(n))-1</math></center> | ||
+ | for all <math>m, n\in\mathbb{N}</math>. Find all possible values of <math>f(2007).</math> | ||
+ | (<math>\mathbb{N}</math> denotes the set of all integers.) |
Revision as of 07:30, 3 August 2023
Problem
(Bulgaria) Consider those functions which satisfy the condition
for all . Find all possible values of
( denotes the set of all integers.)