{
  "abstract": "The 150 years old Sylvester's conjecture asserts that every prime $p\\equiv 4,7,8\\mod 9$ is the sum of two rational cubes. Recently, a proof of this old problem is obtained by the work of mine for the case 4,7 \\cite{Yin} and the work of Burungale-Tian for the case 8 \\cite{BT}. In this paper we give a shorter proof by deep mining my result in \\cite{Yin} combining with the ideas of my previous work on case 8 in \\cite{Yin8}. In particular, we use the ordinary trace and the Kronecker congruence of modular functions, but do not use the $\\sqrt{-3}$-division boundary and Fermat isogeny as in \\cite{BT}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08015",
  "author_total": 1,
  "authors": [
    {
      "name": "Hongbo Yin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7cxd6n6j394dq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08015",
  "fulltext_url": null,
  "id": "7cxd6n6j394dq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08015",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220992999",
  "pdf_url": "https://arxiv.org/pdf/2610.08015",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7cxd6n6j394dq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.08015",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08015"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A concise proof of the 8 case of Sylvester's conjecture",
  "title_text": "A concise proof of the 8 case of Sylvester's conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/7cxd6n6j394dq",
  "venue": "arXiv",
  "versions": []
}