On Unique Additive Representations of Positive Integers and Some Close Problems
| dc.creator | Shevelev, Vladimir | |
| dc.date | 2008-11-03 | |
| dc.date | 2008-12-02 | |
| dc.date.accessioned | 2026-07-07T12:08:03Z | |
| dc.date.available | 2026-07-07T12:08:03Z | |
| dc.description | 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. | |
| dc.description | 14 pages; removing of the last section (Section 10) in view I found an error in proof. in proof | |
| dc.identifier | https://arxiv.org/abs/0811.0290 | |
| dc.identifier | http://arxiv.org/abs/0811.0290 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209182 | |
| dc.subject | Number Theory | |
| dc.subject | 11P81 | |
| dc.title | On Unique Additive Representations of Positive Integers and Some Close Problems | |
| dc.type | text |