Question 52
Prove that the polynomial
$$
P(x) = (x^2 - 8x + 25)(x^2 - 16x + 100) \cdots (x^2 - 8n x + 25 n^2) + 1, \ n \in \mathbb{N}^*,
$$
cannot be written as the product of two polynomials with integer coefficients of degree greater or equal to 1.
$$
P(x) = (x^2 - 8x + 25)(x^2 - 16x + 100) \cdots (x^2 - 8n x + 25 n^2) + 1, \ n \in \mathbb{N}^*,
$$
cannot be written as the product of two polynomials with integer coefficients of degree greater or equal to 1.