{
  "abstract": "A set $\\{a,b,c\\}$ of distinct positive integers is called a Diophantine triple if $ab+1$, $ac+1$, and $bc+1$ are perfect squares. Dujella formulated the conjecture that the only integral $x$-coordinates on the attached elliptic curve $$y^2=(ax+1)(bx+1)(cx+1)$$ are $0,d_-,d_+$, together with $-1$ when the triple contains $1$, where $d_{\\pm}=a+b+c+2abc \\pm2\\sqrt{(ab+1)(ac+1)(bc+1)}$. The weaker question was stated as Problem 4.8 in Dujella's list of open problems: must every integral point with $x\\ne-1$ make $ax+1$, $bx+1$, and $cx+1$ all perfect squares? We construct infinitely many triples $\\{5,115,c\\}$ admitting an integral point with $x\\ne-1$ for which all three factors are nonsquares.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22635",
  "author_total": 2,
  "authors": [
    {
      "name": "Ana Jurasić"
    },
    {
      "name": "Matej Jurasić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7tyr9bd7wx5sk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22635",
  "fulltext_url": null,
  "id": "7tyr9bd7wx5sk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22635",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7204169142",
  "pdf_url": "https://arxiv.org/pdf/2608.22635",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7tyr9bd7wx5sk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2608.22635",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22635"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Counterexamples to Dujella's conjecture on integral points on the elliptic curve attached to a Diophantine triple",
  "title_text": "Counterexamples to Dujella's conjecture on integral points on the elliptic curve attached to a Diophantine triple",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/7tyr9bd7wx5sk",
  "venue": "arXiv",
  "versions": []
}