{
  "abstract": "A classical Pythagorean run is an identity in which a block of consecutive squares is equal to the immediately following block of consecutive squares. Boardman's construction gives such a run for every prescribed length. We consider a cubic analogue in which the second block is allowed to have common difference 2. We prove that there are infinitely many positive integer triples \\((m,A,B)\\), with \\(B>A+2m-1\\), such that $$ \\sum_{j=0}^{2m-1}(A+j)^3 = \\sum_{j=0}^{m-1}(B+2j)^3. $$ An explicit infinite family is obtained from the Pell-type equation $$ 48329z^2-156m^2=161, $$ which reduces to a generalized Pell equation in normalized form. The ordering condition ensures that the step-2 progression begins strictly after the consecutive block ends. The resulting sequence of half-lengths satisfies an explicit second-order linear recurrence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09714",
  "author_total": 1,
  "authors": [
    {
      "name": "Anatoly Eydelzon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/80ezykh5rs4ck.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09714",
  "fulltext_url": null,
  "id": "80ezykh5rs4ck",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09714",
  "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",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7212181302",
  "pdf_url": "https://arxiv.org/pdf/2609.09714",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/80ezykh5rs4ck.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.09714",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09714"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "From Pythagorean Runs to Pell-Generated Cubic Runs",
  "title_text": "From Pythagorean Runs to Pell-Generated Cubic Runs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/80ezykh5rs4ck",
  "venue": "arXiv",
  "versions": []
}