IMC 2008 Day 2 P1 - Polynomial divisor
Source: Problem 1
July 28, 2008
algebrapolynomialmodular arithmeticrationumber theoryrelatively primeIMC
Problem Statement
Let be positive integers and suppose that the polynomial x^{2k}\minus{}x^k\plus{}1 divides x^{2n}\plus{}x^n\plus{}1. Prove that x^{2k}\plus{}x^k\plus{}1 divides x^{2n}\plus{}x^n\plus{}1.