IMO Shortlist 1984 problem 11

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

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IMO Shortlist 1984 problem 11