IMO 2011 Shortlist N6
Let P(x) and Q(x) be two polynomials with integer coefficients such that no nonconstant polynomial with rational coeffic...
Category: Number Theory
Problem
Let P(x) and Q(x) be two polynomials with integer coefficients such that no nonconstant polynomial with rational coefficients divides both P(x) and Q(x). Suppose that for every positive integer n the integers P(n) and Q(n) are positive, and 2Q(n) − 1 divides 3P(n) − 1. Prove that Q(x) is a constant polynomial.