KöMaL 2008 B4111

Let $n$ be a positive integer, and let $a_1$,$a_2$,...,$a_n$ be pairwise different integers. Prove that the polynomial $(x-a_1)(x-a_2) \ldots (x-a_n)-1$ cannot be expressed as a product of two polynomials of integer coefficients whose degrees are at least one.