On a problem of Nathanson on non-minimal additive complements
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917733955796992 |
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| author | Chen, Shi--Qiang Ding, Yuchen |
| author_facet | Chen, Shi--Qiang Ding, Yuchen |
| contents | Let $C$ and $W$ be two sets of integers. If $C+W=\mathbb{Z}$, then $C$ is called an additive complement to $W$. We further call $C$ a minimal additive complement to $W$ if no proper subset of $C$ is an additive complement to $W$. Answering a problem of Nathanson in part, we give sufficient conditions of $W$ which has no minimal additive complements. Our result also extends the prior result of Chen and Yang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a problem of Nathanson on non-minimal additive complements Chen, Shi--Qiang Ding, Yuchen Number Theory Let $C$ and $W$ be two sets of integers. If $C+W=\mathbb{Z}$, then $C$ is called an additive complement to $W$. We further call $C$ a minimal additive complement to $W$ if no proper subset of $C$ is an additive complement to $W$. Answering a problem of Nathanson in part, we give sufficient conditions of $W$ which has no minimal additive complements. Our result also extends the prior result of Chen and Yang. |
| title | On a problem of Nathanson on non-minimal additive complements |
| topic | Number Theory |
| url | https://arxiv.org/abs/2407.04388 |