{
  "abstract": "We discuss local properties of the classical Fibonacci and Lucas sequences, characterising in both cases those primes~$p$ for which the~$p$-part satisfies the Dold congruences or is realizable. We calculate an exact `repair' multiplier in each case and determine the relative prime densities of the Dold, realizable, almost Dold, and almost realizable prime sets. In that order, the four densities are~$(\\frac34,\\frac13,1,\\frac13)$ for the Lucas sequence and~$(\\frac12,\\frac12,1,1)$ for the Fibonacci sequence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24544",
  "author_total": 4,
  "authors": [
    {
      "name": "Sompong Chuysurichay"
    },
    {
      "name": "Sawian Jaidee"
    },
    {
      "name": "Chatchawan Panraksa"
    },
    {
      "name": "Thomas Ward"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5frgzwhhzkack.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24544",
  "fulltext_url": null,
  "id": "5frgzwhhzkack",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24544",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214040976",
  "pdf_url": "https://arxiv.org/pdf/2609.24544",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5frgzwhhzkack.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24544",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24544"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The local Dold congruence for Fibonacci and Lucas sequences",
  "title_text": "The local Dold congruence for Fibonacci and Lucas sequences",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/5frgzwhhzkack",
  "venue": "arXiv",
  "versions": []
}