1

Part of 2008 IMC

Problems(2)

IMC 2008 Day 1 P1

Source:

Find all continuous functions

f: \mathbb{R}\to \mathbb{R}

such that f(x)-f(y)\in \mathbb{Q} \text{ for all } x-y\in\mathbb{Q}

functionalgebrafunctional equationIMCcollege contests

IMC 2008 Day 2 P1 - Polynomial divisor

Source: Problem 1

n, k

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.

algebrapolynomialmodular arithmeticrationumber theoryrelatively primeIMC