IMO Shortlist 1999 problem N6
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
.
%V0
Prove that for every real number $M$ 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 $M$.
Source: Međunarodna matematička olimpijada, shortlist 1999
Školjka 
