{
  "abstract": "In this note, we study the infinite reciprocal sum $\\sum_{k=n}^{\\infty}1/B_k^4$ involving the fourth powers of balancing numbers $B_n$. We show that, for every $n\\geq2$, \\begin{equation*} \\left\\lfloor \\left( \\sum_{k=n}^{\\infty}\\frac{1}{B_k^4} \\right)^{-1} \\right\\rfloor = B_n^4-B_{n-1}^4 -\\left\\lceil\\frac{B_{2n-1}}{280}\\right\\rceil +\\varepsilon_n, \\end{equation*} where $\\varepsilon_n=1$ if $n\\equiv1\\pmod{12}$ and $\\varepsilon_n=0$ otherwise. This result extends the corresponding reciprocal-sum result for Fibonacci numbers due to Hwang, Park and Song to balancing numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31548",
  "author_total": 3,
  "authors": [
    {
      "name": "Subhasis Panda"
    },
    {
      "name": "Aditya Kumar Dash"
    },
    {
      "name": "Utkal Keshari Dutta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d46pc205c4a0x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31548",
  "fulltext_url": null,
  "id": "d46pc205c4a0x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31548",
  "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|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7214579387",
  "pdf_url": "https://arxiv.org/pdf/2609.31548",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d46pc205c4a0x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31548",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31548"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the infinite sum of reciprocals of the fourth powers of balancing numbers",
  "title_text": "On the infinite sum of reciprocals of the fourth powers of balancing numbers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/d46pc205c4a0x",
  "venue": "arXiv",
  "versions": []
}