{
  "abstract": "We prove that if the smallest modulus of a covering system is a prime $q \\ge 11$, then the sum of the reciprocals of the moduli is at least $1+10^{-28}$. This improves on a previous more general bound of the first two authors in this particular case. We also show that it is impossible to construct a covering system using distinct multiples of $q$ as moduli. Finally, we show as a corollary that it is impossible to construct $10$ distinct covering systems with the property that no modulus is used in more than one of the covering systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34541",
  "author_total": 3,
  "authors": [
    {
      "name": "Michael Filaseta"
    },
    {
      "name": "Alexandros Kalogirou"
    },
    {
      "name": "Jonah Klein"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2cfmgderwbhn9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34541",
  "fulltext_url": null,
  "id": "2cfmgderwbhn9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34541",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223882725",
  "pdf_url": "https://arxiv.org/pdf/2610.34541",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2cfmgderwbhn9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34541",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34541"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Results for distinct covering systems with a prime minimum modulus $q \\ge 11$",
  "title_text": "Results for distinct covering systems with a prime minimum modulus q ≥ 11",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/2cfmgderwbhn9",
  "venue": "arXiv",
  "versions": []
}