{
  "abstract": "In this paper, we study the $p$-adic zeros of the Tribonacci sequence $T_n$, for a prime $p$. In particular, we complete the analysis that was done in a 2024 paper of Yuri Bilu by investigating the case of $p=11$. In addition, we investigate the primes $p$ for which at the first two values $T_n$ and $T_{n-1}$ which are both divisible by $p$, both of these are actually divisible by $p^2$, proving under the assumption of a generalisation of the $abc$ conjecture that there are infinitely many $p$ which are not such.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22364",
  "author_total": 3,
  "authors": [
    {
      "name": "Liam Baker"
    },
    {
      "name": "Florian Luca"
    },
    {
      "name": "Kerry Porrill"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dp9eba3rdr921.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22364",
  "fulltext_url": null,
  "id": "dp9eba3rdr921",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22364",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214021957",
  "pdf_url": "https://arxiv.org/pdf/2609.22364",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dp9eba3rdr921.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22364",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22364"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On periods of the Tribonacci sequence modulo primes",
  "title_text": "On periods of the Tribonacci sequence modulo primes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/dp9eba3rdr921",
  "venue": "arXiv",
  "versions": []
}