Multiples beginning with 2008
Source: Brazilian Math Olympiad 2008, Problem 1
October 28, 2008
pigeonhole principlenumber theory unsolvednumber theory
Problem Statement
A positive integer is dapper if at least one of its multiples begins with . For example, is dapper because is a multiple of and begins with . Observe that 200858 \equal{} 28694\times 7.
Prove that every positive integer is dapper.