Difference between revisions of "2009 IMO Problems/Problem 3"
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Revision as of 13:03, 10 July 2012
Problem
Suppose that is a strictly increasing sequence of positive integers such that the subsequences
![$s_{s_1},s_{s_2},s_{s_3},\ldots$](http://latex.artofproblemsolving.com/5/7/8/578b37a84533d816f7bb21a83536aa751620abc2.png)
![$s_{s_1+1},s_{s_2+1},s_{s_3+1},\ldots$](http://latex.artofproblemsolving.com/9/4/3/943bd637535b539c3df40146ad44f3ab658db56c.png)
are both arithmetic progressions. Prove that the sequence is itself an arithmetic progression.
Author: Gabriel Carroll, USA