IMO Shortlist 2000 problem A1


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2. travnja 2012.
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Let a, b, c be positive real numbers so that abc = 1. Prove that
\left( a - 1 + \frac 1b \right) \left( b - 1 + \frac 1c \right) \left( c - 1 + \frac 1a \right) \leq 1.
Izvor: Međunarodna matematička olimpijada, shortlist 2000