A connection between covers of the integers and unit fractions
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2004-11-15 | |
| dc.date | 2006-07-26 | |
| dc.date.accessioned | 2026-07-07T06:39:00Z | |
| dc.date.available | 2026-07-07T06:39:00Z | |
| dc.description | For integers a and n>0, let a(n) denote the residue class {x\in Z: x=a (mod n)}. Let A be a collection {a_s(n_s)}_{s=1}^k of finitely many residue classes such that A covers all the integers at least m times but {a_s(n_s)}_{s=1}^{k-1} does not. We show that if n_k is a period of the covering function w_A(x)=|{1\le s\le k: x\in a_s(n_s)}| then for any r=0,...,n_k-1 there are at least m integers in the form $\sum_{s\in I}1/n_s-r/n_k$ with I contained in {1,...,k-1}. | |
| dc.description | 9 pages. To appear in Adv. in Appl. Math | |
| dc.identifier | https://arxiv.org/abs/math/0411305 | |
| dc.identifier | http://arxiv.org/abs/math/0411305 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100939 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B25; 11B75; 11D68; 05A05 | |
| dc.title | A connection between covers of the integers and unit fractions | |
| dc.type | text |