BALKAN-SL 2013 A3

Prove that the polynomial $P (x) = (x^2- 8x + 25) (x^2 - 16x + 100) ... (x^2 - 8nx + 25n^2)- 1$ , $n \in N^*$ , cannot be written as the product of two polynomials with integer coefficients of degree greater or equal to $1$ .