IMO Shortlist 2009 problem A6


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2. travnja 2012.
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Suppose that s_1,s_2,s_3, \ldots is a strictly increasing sequence of positive integers such that the sub-sequences 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.

Proposed by Gabriel Carroll, USA
Izvor: Međunarodna matematička olimpijada, shortlist 2009