Counting numbers divisible by their digital product
Source: German TST 2024, Test 7, Problem 2
May 15, 2024
number theorynumber theory proposedDigitsproduct of digitsDivisibility
Problem Statement
Show that there exists a real constant with the following property:
For any positive integer , there are at least positive integers with exactly decimal digits, which are divisible by the product of their digits. (In particular, these digits are all non-zero.)
Proposed by Jean-Marie De Koninck and Florian Luca