MathDB
Common divisors of symilar polynomials

Source: Italian National Olympiad 2007, problem 2

May 13, 2007
algebrapolynomialmodular arithmeticalgebra proposed

Problem Statement

We define two polynomials with integer coefficients P,Q to be similar if the coefficients of P are a permutation of the coefficients of Q. a) if P,Q are similar, then P(2007)−Q(2007)P(2007)-Q(2007) is even b) does there exist an integer k>2k > 2 such that k∣P(2007)−Q(2007)k \mid P(2007)-Q(2007) for all similar polynomials P,Q?
Back to ProblemsView on AoPS