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

2009 IMO Problems/Problem 3

Revision as of 13:03, 10 July 2012 by JBL (talk | contribs)

Problem

Suppose that $s_1,s_2,s_3,\ldots$ is a strictly increasing sequence of positive integers such that the subsequences

$s_{s_1},s_{s_2},s_{s_3},\ldots$ and $s_{s_1+1},s_{s_2+1},s_{s_3+1},\ldots$

are both arithmetic progressions. Prove that the sequence $s_1,s_2,s_3,\ldots$ is itself an arithmetic progression.

Author: Gabriel Carroll, USA

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2009_IMO_Problems/Problem_3&oldid=47603"