IMO 2022 Shortlist A7
For a positive integer n we denote by spnq the sum of the digits of n. Let Ppxq “ xn an´1xn´1 ¨¨¨a1xa0 be a polynomial, ...
Category: Algebra
Problem
For a positive integer n we denote by spnq the sum of the digits of n. Let Ppxq “
xn
an´1xn´1 ¨¨¨a1xa0 be a polynomial, where n ě 2 and ai is a positive integer for all
0 ď i ď n ´ 1. Could it be the case that, for all positive integers k, spkq and spPpkqq have the
same parity?
(Belarus)