{
  "abstract": "In an article, S. Adlaj showed the construction of the $F_4 = 65\\,537$-gon ($F_4$ a Fermat prime). By extending the author's method to cases where the multiplicative group is not of order $2^n$ but has an additional prime factor, I here construct the $641$-gon. $641$ is the smaller prime factor of the composite Fermat number $F_5 = 2^{2^5} + 1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.04000",
  "author_total": 1,
  "authors": [
    {
      "name": "Helmut Ruhland"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0zh9jagts396y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.04000",
  "fulltext_url": null,
  "id": "0zh9jagts396y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.04000",
  "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",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7167574245",
  "pdf_url": "https://arxiv.org/pdf/2607.04000",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0zh9jagts396y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2607.04000",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.04000"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Constructing the $\\mathbf{2^{2^5} + 1 = F_5}$-gon, the first step: the 641-gon",
  "title_text": "Constructing the 2^2^5 + 1 = F_5-gon, the first step: the 641-gon",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/0zh9jagts396y",
  "venue": "arXiv",
  "versions": []
}