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

2013 IMO Problems/Problem 1

Revision as of 01:34, 11 October 2013 by DANCH (talk | contribs) (Created page with "==Problem== Prove that for any pair of positive integers <math>k</math> and <math>n</math>, there exist <math>k</math> positive integers <math>m_1,m_2,...,m_k</math> (not necessa...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Prove that for any pair of positive integers $k$ and $n$, there exist $k$ positive integers $m_1,m_2,...,m_k$ (not necessarily different) such that

$1+\frac{2^k-1}{n}=(1+\frac{1}{m_1})(1+\frac{1}{m_2})...(1+\frac{1}{m_k})$.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2013_IMO_Problems/Problem_1&oldid=57247"