{
  "abstract": "A positive integer $n$ is called a practical number if every positive integer less than or equal to $n$ can be expressed as a sum of distinct positive divisors of $n$. In this paper, we study an open conjecture proposed by Wang and Sun concerning the quadratic representations of practical numbers. Specifically, we provide a short proof of the second part of the conjecture, demonstrating that for any positive integers $b$ and $c$ with $2 \\nmid b$ and $2 \\mid c$, there exists an integer $n$ satisfying $1 < n \\le \\max\\{b, c\\}$ such that $n^2 + bn + c$ is a practical number. Combined with the work of Somu, Li, and Kukla, this completely settles the conjecture of Wang and Sun.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25591",
  "author_total": 1,
  "authors": [
    {
      "name": "Ting Hon Stanford Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2mmm7t289stn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25591",
  "fulltext_url": null,
  "id": "b2mmm7t289stn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25591",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7204439737",
  "pdf_url": "https://arxiv.org/pdf/2608.25591",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2mmm7t289stn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2608.25591",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25591"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Short Proof of a Conjecture Regarding Quadratic Representations of Practical Numbers",
  "title_text": "A Short Proof of a Conjecture Regarding Quadratic Representations of Practical Numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/b2mmm7t289stn",
  "venue": "arXiv",
  "versions": []
}