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

Revision as of 07:30, 3 August 2023 by Dondee123 (talk | contribs)

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.)

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2007_IMO_Shortlist_Problems/A2&oldid=196378"