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(x^2-8x+25)(x^2-16x+100)...(x^2-8nx+25n^2)-1 not product of 2 integer polyn.

Source: Balkan MO Shortlist 2013 A3 BMO

March 9, 2020
algebrapolynomialfactoring polynomialsInteger Polynomial

Problem Statement

Prove that the polynomial P(x)=(x2−8x+25)(x2−16x+100)...(x2−8nx+25n2)−1P (x) = (x^2- 8x + 25) (x^2 - 16x + 100) ... (x^2 - 8nx + 25n^2)- 1, n∈N∗n \in N^*, cannot be written as the product of two polynomials with integer coefficients of degree greater or equal to 11.
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