IMO 2021 Shortlist N8
For a polynomial Ppxq with integer coefficients let P1 pxq “ Ppxq and Pk1 pxq “ PpPk pxqq for k ě1. Find all positive in...
Category: Number Theory
Problem
For a polynomial Ppxq with integer coefficients let P1 pxq “ Ppxq and Pk`1 pxq “ PpPk pxqq for k ě1. Find all positive integers n for which there exists a polynomial Ppxq with integer coefficients such that for every integer m ě 1, the numbers Pm p1q,...,Pm pnq leave exactly rn{2m s distinct remainders when divided by n. Shortlisted problems – solutions 11 This page is intentionally left blank 12 Saint-Petersburg — Russia, 16th–24th July 2021 Shortlisted problems – solutions 13