{
  "abstract": "We classify all $D(u^2)$-triples of triangular numbers whose smallest element is $T_{4u-1}$ or $T_{4u}$. We study the regularity of $D(N)$-triples of triangular numbers. We also show that infinitely many positive integers $u$ admit an all-triangular $D(u^2)$-quadruple. For every positive integer $k$, triangular number $T_{16k^2-1}$ belongs to infinitely many $D(u^2)$-quadruples of triangular numbers with distinct positive integer parameters $u$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28018",
  "author_total": 1,
  "authors": [
    {
      "name": "Pavao Radić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7awm4bhwj3ky6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28018",
  "fulltext_url": null,
  "id": "7awm4bhwj3ky6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28018",
  "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.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214193693",
  "pdf_url": "https://arxiv.org/pdf/2609.28018",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7awm4bhwj3ky6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28018",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28018"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On some $D(u^2)$-triples and quadruples of triangular numbers",
  "title_text": "On some D(u^2)-triples and quadruples of triangular numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/7awm4bhwj3ky6",
  "venue": "arXiv",
  "versions": []
}