{
  "abstract": "We determine the odd primes $p$ for which the number of distinct prime divisors of $d-x^2$ is at most $2$ for every positive odd integers $x\\leq\\sqrt{p}$. We also determine the odd primes $p$ for which the number of distinct prime divisors of $2p-x^2$ is at most $2$ for every positive even integers $x\\leq\\sqrt{2p}$. To this end, we show that these properties of $p$ and $2p$ impose restrictions on the class numbers and fundamental units of the real quadratic fields ${\\mathbb Q}(\\sqrt{p})$ and ${\\mathbb Q}(\\sqrt{2p})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29347",
  "author_total": 1,
  "authors": [
    {
      "name": "Stéphane R. Louboutin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48kfeapy3dzmc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29347",
  "fulltext_url": null,
  "id": "48kfeapy3dzmc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29347",
  "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",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7223197486",
  "pdf_url": "https://arxiv.org/pdf/2610.29347",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/48kfeapy3dzmc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29347",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29347"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ideal class groups of certain real quadratic number fields and factorizations of values of certain quadratic polynomials",
  "title_text": "Ideal class groups of certain real quadratic number fields and factorizations of values of certain quadratic polynomials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/48kfeapy3dzmc",
  "venue": "arXiv",
  "versions": []
}