Question 133
Let $n \geq 2$ be a natural number. Show that the polynomial
$$
\left(x^{2}-1^{2}\right)\left(x^{2}-2^{2}\right)\left(x^{2}-3^{2}\right) \cdots\left(x^{2}-n^{2}\right)+1
$$
cannot be written as a product of two non-constant polynomials with integer coefficients.
$$
\left(x^{2}-1^{2}\right)\left(x^{2}-2^{2}\right)\left(x^{2}-3^{2}\right) \cdots\left(x^{2}-n^{2}\right)+1
$$
cannot be written as a product of two non-constant polynomials with integer coefficients.