Question 2
If $a_1,a_2,\ldots,a_n$ are distinct integers, prove that
$$(x-a_1)(x-a_2)\cdots(x-a_n)-1$$
cannot be expressed as a product of two polynomials, each with integer coefficients and of degree at least $1$.
$$(x-a_1)(x-a_2)\cdots(x-a_n)-1$$
cannot be expressed as a product of two polynomials, each with integer coefficients and of degree at least $1$.