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

2001 IMO Shortlist Problems/A5

Revision as of 18:16, 20 August 2008 by Minsoens (talk | contribs) (New page: == Problem == Find all positive integers <math>a_1, a_2, \ldots, a_n</math> such that <center><math>\frac {99}{100} = \frac {a_0}{a_1} + \frac {a_1}{a_2} + \cdots + \frac {a_{n - 1}}{a_n},...)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Find all positive integers $a_1, a_2, \ldots, a_n$ such that

$\frac {99}{100} = \frac {a_0}{a_1} + \frac {a_1}{a_2} + \cdots + \frac {a_{n - 1}}{a_n},$

where $a_0 = 1$ and $(a_{k + 1} - 1)a_{k - 1} \geq a_k^2(a_k - 1)$ for $k = 1,2,\ldots,n - 1$.

Solution

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

Resources

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2001_IMO_Shortlist_Problems/A5&oldid=27499"