MathDB
LIMIT 2020 P5

Source: LIMIT 2020

April 11, 2020
algebrapolynomialalgorithm

Problem Statement

Let P(x),Q(x)P(x),Q(x) be monic polynomials with integer coeeficients. Let an=n!+na_n=n!+n for all natural numbers nn. Show that if P(an)Q(an)\frac{P(a_n)}{Q(a_n)} is an integer for all positive integer nn then P(n)Q(n)\frac{P(n)}{Q(n)} is an integer for every integer n≠0n\neq0. \\ Hint (given in question): Try applying division algorithm for polynomials
Back to ProblemsView on AoPS