MathDB
Mozart numbers

Source: MEMO 2016 T7

August 25, 2016
number theorynumber theory proposedParityDigits

Problem Statement

A positive integer nn is Mozart if the decimal representation of the sequence 1,2,,n1, 2, \ldots, n contains each digit an even number of times.
Prove that: 1. All Mozart numbers are even. 2. There are infinitely many Mozart numbers.