Art of Problem Solving
Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2007 IMO Shortlist Problems/A2: Difference between revisions

Newer edit →
Dondee123 (talk | contribs)
editor
44 edits
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..."
 
Dondee123 (talk | contribs)
editor
44 edits
Tag: Blanking
Line 1: Line 1:
== 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 <math>m</math>, <math>n </math>\in\mathbb{N}<math>. Find all possible values of </math>f(2007)<math>.
(</math>\mathbb{N}$ denotes the set of all positive integers.)

Revision as of 07:20, 3 August 2023

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2007_IMO_Shortlist_Problems/A2&oldid=196377"