MathDB
integer polynomials, p(x)q(x) - 2015 has at least 33 different integer roots

Source: Irmo 2015 p2 q9

September 16, 2018
algebrapolynomialinteger rootInteger Polynomial

Problem Statement

Let p(x)p(x) and q(x)q(x) be non-constant polynomial functions with integer coeffcients. It is known that the polynomial p(x)q(x)āˆ’2015p(x)q(x) - 2015 has at least 3333 different integer roots. Prove that neither p(x)p(x) nor q(x)q(x) can be a polynomial of degree less than three.