Digitally Divisible Integers
Source: Canadian Mathematical Olympiad - 1984 - Problem 3.
June 26, 2011
inductionnumber theory unsolvednumber theory
Problem Statement
An integer is digitally divisible if both of the following conditions are fulfilled:
None of its digits is zero;
It is divisible by the sum of its digits
e.g. is digitally divisible. Show that there are infinitely many digitally divisible integers.