IMO Shortlist 2008 problem N2


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2. travnja 2012.
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Let a_1, a_2, \ldots, a_n be distinct positive integers, n\ge 3. Prove that there exist distinct indices i and j such that a_i + a_j does not divide any of the numbers 3a_1, 3a_2, \ldots, 3a_n.

Proposed by Mohsen Jamaali, Iran
Izvor: Međunarodna matematička olimpijada, shortlist 2008