IMO Shortlist 1999 problem N6
Dodao/la:
arhiva2. travnja 2012. Prove that for every real number
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
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](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
.
%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 $M$.
Izvor: Međunarodna matematička olimpijada, shortlist 1999