IMO ShortList 1999, number theory problem 6
Source: IMO ShortList 1999, number theory problem 6
November 13, 2004
algebramodular arithmeticarithmetic sequenceDivisibilitysum of digitsIMO Shortlist
Problem Statement
Prove that for every real number there exists an infinite arithmetic progression such that:
- each term is a positive integer and the common difference is not divisible by 10
- the sum of the digits of each term (in decimal representation) exceeds .