IMO Shortlist 1984 problem 11
Dodao/la:
arhiva2. travnja 2012. Let
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
be a positive integer and
![a_1, a_2, \dots , a_{2n}](/media/m/7/5/9/7595276e4488a0c37ae00ccf590f8d7d.png)
mutually distinct integers. Find all integers
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
satisfying
%V0
Let $n$ be a positive integer and $a_1, a_2, \dots , a_{2n}$ mutually distinct integers. Find all integers $x$ satisfying
$$(x - a_1) \cdot (x - a_2) \cdots (x - a_{2n}) = (-1)^n(n!)^2.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1984