Difference between revisions of "2009 IMO Problems/Problem 3"

(Created page with '== Problem == Suppose that <math>s_1,s_2,s_3,\ldots</math> is a strictly increasing sequence of positive integers such that the subsequences <center> <math>s_{s_1},s_{s_2},s_{…')
 
m
Line 8: Line 8:
  
 
''Author: Gabriel Carroll, USA''
 
''Author: Gabriel Carroll, USA''
 
--[[User:Bugi|Bugi]] 10:22, 23 July 2009 (UTC) Bugi
 

Revision as of 13:03, 10 July 2012

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