Problem

Source: 44th International Tournament of Towns, Junior A-Level P3, Spring 2023

Tags: number theory, decimal representation



Let us call a positive integer pedestrian if all its decimal digits are equal to 0 or 1. Suppose that the product of some two pedestrian integers also is pedestrian. Is it necessary in this case that the sum of digits of the product equals the product of the sums of digits of the factors? Viktor Kleptsyn, Konstantin Knop