{
  "abstract": "The solution of the Diophantine equation ay^2=b(x^k-c^k) is studied in different cases of k. Methods are proposed for different cases of k, which are convenient for computer algorithm implementation. The original equation is reduced to lower-degree equations, which can improve the efficiency in searching possible integer solutions. A sufficient condition of the unsolvability of ay^2=b(x^2n-c^2n) is presented.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00119",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaodong Zhuang"
    },
    {
      "name": "Nikos E. Mastorakis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4tqb90gf3mmd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00119",
  "fulltext_url": null,
  "id": "d4tqb90gf3mmd",
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  "landing_url": "https://arxiv.org/abs/2610.00119",
  "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"
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      "openalex",
      "2608|Algebraic Geometry and Number Theory"
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  "openalex": "W7216549963",
  "pdf_url": "https://arxiv.org/pdf/2610.00119",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4tqb90gf3mmd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00119",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00119"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Some Methods to Solve the Diophantine Equation ay^2=b(x^k-c^k)",
  "title_text": "Some Methods to Solve the Diophantine Equation ay^2=b(x^k-c^k)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/d4tqb90gf3mmd",
  "venue": "arXiv",
  "versions": []
}