sum of digits is multiple of 2011
Source: 2011 Romania NMO VIII p4
August 15, 2024
number theorysum of digits
Problem Statement
A positive integer will be called typical if the sum of its decimal digits is a multiple of .
a) Show that there are infinitely many typical numbers, each having at least multiples which are also typical numbers.
b) Does there exist a positive integer such that each of its multiples is typical?