Problem

Source: 2022 Czech and Slovak Olympiad III A p2

Tags: number theory, palindromes, palindrome



We say that a positive integer $k$ is fair if the number of $2021$-digit palindromes that are a multiple of $k$ is the same as the number of $2022$-digit palindromes that are a multiple of $k$. Does the set $M = \{1, 2,..,35\}$ contain more numbers that are fair or those that are not fair? (A palindrome is an integer that reads the same forward and backward.) (David Hruska)