MathDB

7

Part of 2016 Middle European Mathematical Olympiad

Problems(1)

Mozart numbers

Source: MEMO 2016 T7

8/25/2016
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.
number theorynumber theory proposedParityDigits