Difference between revisions of "2007 IMO Shortlist Problems/A2"
(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...") |
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(''Bulgaria'') | (''Bulgaria'') | ||
Consider those functions <math>f:\mathbb{N}\to\mathbb{N}</math> which satisfy the condition | 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 | + | 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.) | ||
| + | |||
| + | == Solution == | ||
Latest 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.)
