On subset sums of $\mathbb{Z}_n^{\times}$ which are equally distributed modulo $n$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917114614382592 |
|---|---|
| author | Gaitanas, Konstantinos |
| author_facet | Gaitanas, Konstantinos |
| contents | In this note, we provide some results concerning the structure of a set $A\subseteq \mathbb{Z}_n^{\times}$, which has non-empty subset sums equally distributed modulo $n$. Here, $\mathbb{Z}_n^{\times}$ denotes the set which contains all the invertible elements of the ring $\mathbb{Z}_n$. In particular, we prove that if $n=q$ is a power of an odd prime, then $A$ is a union of sets of the form $\{ a\cdot(\pm2^i)\}$. Additionally, we count the number of subsets of $\mathbb{Z}_q^{\times}$ with non-empty subset sums equally distributed modulo $q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14141 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On subset sums of $\mathbb{Z}_n^{\times}$ which are equally distributed modulo $n$ Gaitanas, Konstantinos General Mathematics 11P70 In this note, we provide some results concerning the structure of a set $A\subseteq \mathbb{Z}_n^{\times}$, which has non-empty subset sums equally distributed modulo $n$. Here, $\mathbb{Z}_n^{\times}$ denotes the set which contains all the invertible elements of the ring $\mathbb{Z}_n$. In particular, we prove that if $n=q$ is a power of an odd prime, then $A$ is a union of sets of the form $\{ a\cdot(\pm2^i)\}$. Additionally, we count the number of subsets of $\mathbb{Z}_q^{\times}$ with non-empty subset sums equally distributed modulo $q$. |
| title | On subset sums of $\mathbb{Z}_n^{\times}$ which are equally distributed modulo $n$ |
| topic | General Mathematics 11P70 |
| url | https://arxiv.org/abs/2304.14141 |