{
  "abstract": "Restricted forms of Lagrange's four-square theorem, in which the representing variables are required to satisfy additional arithmetic conditions, have been studied from several points of view. Among the refinements proposed by Zhi-Wei Sun is the conjecture that every nonnegative integer has a representation \\[ N=x^2+y^2+z^2+w^2,\\qquad x,y,z,w\\in\\mathbb Z_{\\ge0}, \\] for which \\[ x\\ \\text{and}\\ x+24y\\ \\text{are perfect squares}. \\] We prove this conjecture for all sufficiently large integers. The proof starts from an elementary parametrization of the two square conditions and combines a semi-linear two-squares sieve with Poisson summation, finite-field cancellation, and switching.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13338",
  "author_total": 1,
  "authors": [
    {
      "name": "Bo He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fdrrm7q9vzah9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13338",
  "fulltext_url": null,
  "id": "fdrrm7q9vzah9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13338",
  "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": "W7213247373",
  "pdf_url": "https://arxiv.org/pdf/2609.13338",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fdrrm7q9vzah9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13338",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13338"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The Strong 24-Conjecture",
  "title_text": "The Strong 24-Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/fdrrm7q9vzah9",
  "venue": "arXiv",
  "versions": []
}