{
  "abstract": "Let $(T_n)_{n\\ge1}$ be the Tribonacci sequence, defined by $T_1=T_2=1$, $T_3=2$, and $T_n=T_{n-1}+T_{n-2}+T_{n-3}$ for $n\\ge4$. In this paper, we study the Tribonacci numbers whose decimal representation is a palindromic concatenation of two distinct repdigits, that is, numbers of the shape $\\overline{d_1\\cdots d_1\\,d_2\\cdots d_2\\,d_1\\cdots d_1}$ with $1\\le d_1\\le9$, $0\\le d_2\\le9$, $d_1\\ne d_2$. We prove that no Tribonacci number is a palindromic concatenation of two distinct repdigits. The proof combines lower bounds for linear forms in logarithms, the Baker-Davenport reduction method, and a finite computational verification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15770",
  "author_total": 2,
  "authors": [
    {
      "name": "Khady Faye"
    },
    {
      "name": "Bernadette Faye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d9tba379xg3cd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15770",
  "fulltext_url": null,
  "id": "d9tba379xg3cd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15770",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221774892",
  "pdf_url": "https://arxiv.org/pdf/2610.15770",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d9tba379xg3cd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15770",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15770"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Tribonacci numbers that are palindromic concatenations of two distinct repdigits",
  "title_text": "Tribonacci numbers that are palindromic concatenations of two distinct repdigits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/d9tba379xg3cd",
  "venue": "arXiv",
  "versions": []
}