2001 Austrian-Polish Mathematics Competition
Source: Problem 7
September 19, 2006
number theory unsolvednumber theory
Problem Statement
Consider the set containing all positive integers whose decimal expansion contains no , and whose sum of the digits divides .
(a) Prove that there exist infinitely many elements in whose decimal expansion contains each digit the same number of times as each other digit.
(b) Explain that for each positive integer there exist an element in having exactly digits.