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PreprintCC BY 4.0arXiv

On a problem of Erdős and Nathanson related to minimal asymptotic bases of order h

  • Shi-Qiang Chen
  • Quan-Hui Yang
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Abstract

Let h≥ 3 be an integer and 0<α<1/h. In this paper, we prove that there exists a minimal asymptotic basis of order h with asymptotic density α. This solves an open problem posed by Erdős and Nathanson in 1988.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026problem,
  title = {{On a problem of Erdős and Nathanson related to minimal asymptotic bases of order $h$}},
  author = {Shi-Qiang Chen and Quan-Hui Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08706},
  eprint = {2609.08706},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08706},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On a problem of Erdős and Nathanson related to minimal asymptotic bases of order h
AU  - Shi-Qiang Chen
AU  - Quan-Hui Yang
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08706
UR  - https://arxiv.org/abs/2609.08706
AB  - Let h≥ 3 be an integer and 0<α<1/h. In this paper, we prove that there exists a minimal asymptotic basis of order h with asymptotic density α. This solves an open problem posed by Erdős and Nathanson in 1988.
ER  -