On Unique Additive Representations of Positive Integers and Some Close Problems

Details On Unique Additive Representations of Positive Integers and Some Close Problems On Unique Additive Representations of Positive Integers and Some Close Problems

2008-11-03

arxiv.org/abs/0811.0290v5

Mathematics

Number Theory

14 pages; removing of the last section (Section 10) in view I found an error in proof. in proof

Scientific paper

Let, for r>=2, (m_r(n)),n>=0, be Moser sequence such that every nonnegative integer is the unique sum of the form s_k+rs_l. In this article we give an explicit decomposition formulas of such form and an unexpectedly simple recursion relation for Moser's numbers. We also study interesting properties of the sequence (rm_r(n-1)+1),n>=1, and its connection with some important problems. In particular, in the case of r=2 this sequence is surprisingly connected with the numbers solving the combinatorial Josephus-Groer problem. We pose also some open questions.

Affiliated with

Also associated with

No associations

Rating

On Unique Additive Representations of Positive Integers and Some Close Problems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On Unique Additive Representations of Positive Integers and Some Close Problems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Unique Additive Representations of Positive Integers and Some Close Problems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-233903