IMO 2011 Shortlist N2
Consider a polynomial P(x) = (x + d1)(x + d2) · ... · (x + d9), where d1, d2,..., d9 are nine distinct integers. Prove t...
Category: Number Theory
Problem
Consider a polynomial P(x) = (x + d1)(x + d2) · ... · (x + d9), where d1, d2,..., d9 are nine distinct integers. Prove that there exists an integer N such that for all integers x ≥ N the number P(x) is divisible by a prime number greater than 20.