IMO Shortlist 1966 problem 2


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2. travnja 2012.
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Given n positive real numbers a_1, a_2, \ldots , a_n such that a_1a_2 \cdots a_n = 1, prove that
(1 + a_1)(1 + a_2) \cdots (1 + a_n) \geq 2^n.
Izvor: Međunarodna matematička olimpijada, shortlist 1966