On complete subsets of the cyclic group
| dc.creator | Hamidoune, Y. O. | |
| dc.creator | Lladó, A. S. | |
| dc.creator | Serra, O. | |
| dc.date | 2007-04-04 | |
| dc.date.accessioned | 2026-07-07T07:54:31Z | |
| dc.date.available | 2026-07-07T07:54:31Z | |
| dc.description | A subset $X$ of an abelian $G$ is said to be {\em complete} if every element of the subgroup generated by $X$ can be expressed as a nonempty sum of distinct elements from $X$. Let $A\subset \Z_n$ be such that all the elements of $A$ are coprime with $n$. Solving a conjecture of Erdős and Heilbronn, Olson proved that $A$ is complete if $n$ is a prime and if $|A|>2\sqrt{n}.$ Recently Vu proved that there is an absolute constant $c$, such that for an arbitrary large $n$, $A$ is complete if $|A|\ge c\sqrt{n},$ and conjectured that 2 is essentially the right value of $c$. We show that $A$ is complete if $|A|> 1+2\sqrt{n-4}$, thus proving the last conjecture. | |
| dc.identifier | https://arxiv.org/abs/0704.0541 | |
| dc.identifier | http://arxiv.org/abs/0704.0541 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126636 | |
| dc.subject | Number Theory | |
| dc.subject | 11B75, 20D60 | |
| dc.title | On complete subsets of the cyclic group | |
| dc.type | text |