MathDB
Q 12

Source:

May 25, 2007
algebrapolynomialGaussPolynomials

Problem Statement

Prove that if the integers a1a_{1}, a2a_{2}, \cdots, ana_{n} are all distinct, then the polynomial (xa1)2(xa2)2(xan)2+1(x-a_{1})^{2}(x-a_{2})^{2}\cdots (x-a_{n})^{2}+1 cannot be expressed as the product of two nonconstant polynomials with integer coefficients.