{
  "abstract": "For binary recurrence sequences, $\\left( y_{k} \\right)_{k \\in \\bbZ}$, arising from the solutions of generalised Pell equations, $X^{2}-dY^{2}=c$, where $y_{0}$ is any positive square and $c=-2^{\\ell}p^{m}$ for an odd prime $p$ and non-negative integers $\\ell$ and $m$, we show that there are at most $4$ distinct squares with $y_{k}$ sufficiently large. From this result, we also show that there are at most $7$ distinct squares when $y_{0}=1,2^{2},\\ldots,7^{2}$, or once $d$ exceeds an explicit lower bound, without any conditions on the size of such squares.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Research in Number Theory, volume 12, article 6 (2026)",
  "arxiv": "2610.35158",
  "author_total": 1,
  "authors": [
    {
      "name": "Paul M Voutier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8dr9pefr4twaq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35158",
  "fulltext_url": null,
  "id": "8dr9pefr4twaq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35158",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.35158",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8dr9pefr4twaq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35158",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35158"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bounds on the number of squares in recurrence sequences: $y_{0}=b^{2}$ (II)",
  "title_text": "Bounds on the number of squares in recurrence sequences: y_0=b^2 (II)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/8dr9pefr4twaq",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1007/s40993-025-00696-w",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}