IMO Shortlist 2000 problem A1
Dodao/la:
arhiva2. travnja 2012. Let
![a, b, c](/media/m/9/e/9/9e9dfe78930065fbe5a777e9b07c27c4.png)
be positive real numbers so that
![abc = 1](/media/m/c/8/a/c8a9e3a4e666d28bd7610ebdd4e531fb.png)
. Prove that
%V0
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