IMO Shortlist 1966 problem 2
Dodao/la:
arhiva2. travnja 2012. Given
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
positive real numbers
![a_1, a_2, \ldots , a_n](/media/m/0/a/8/0a84730daafb8c167c30263462061224.png)
such that
![a_1a_2 \cdots a_n = 1](/media/m/a/9/f/a9fafb9d3d0712ad1b6d096a9967e33d.png)
, prove that
%V0
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