{
  "abstract": "A set of $m$ distinct positive integers is called a Diophantine $m$-tuple if the product of any two distinct elements, increased by one, is a perfect square. A Diophantine quadruple $\\{a,b,c,d\\}$ with $a<b<c<d$ is called regular if $$d=a+b+c+2abc+2\\sqrt{(ab+1)(ac+1)(bc+1)}.$$ We prove that every irregular Diophantine quadruple satisfies $c<10^{338}$ and $d<10^{10^{24}}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18912",
  "author_total": 2,
  "authors": [
    {
      "name": "Bo He"
    },
    {
      "name": "Alain Togbe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahhk5sea833e4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18912",
  "fulltext_url": null,
  "id": "ahhk5sea833e4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18912",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GM"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222024688",
  "pdf_url": "https://arxiv.org/pdf/2610.18912",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ahhk5sea833e4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.18912",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18912"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic Geometry and Number Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "There are only finitely many irregular Diophantine quadruples",
  "title_text": "There are only finitely many irregular Diophantine quadruples",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/ahhk5sea833e4",
  "venue": "arXiv",
  "versions": []
}