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

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''Author: Gabriel Carroll, USA''
 
''Author: Gabriel Carroll, USA''
 
--[[User:Bugi|Bugi]] 10:22, 23 July 2009 (UTC) Bugi
 

Latest 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

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