{
  "abstract": "The Diophantine equation $F_n^x+F_m^y=2^a,$ where $F_k$ denotes the $k$-th Fibonacci number and $n,m,a\\in \\mathbb{Z}_{\\geq0}$, has attracted attention in recent years. The cases $(x,y)=(1,1)$ and $(x,y)=(2,2)$ were completely resolved by Bravo and Luca, and by Jeong and Park, respectively. In this note, we investigate the mixed exponent case $(x,y)=(2,1)$ and we completely determine all nonnegative integer solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18894",
  "author_total": 1,
  "authors": [
    {
      "name": "Sagar Mandal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38j2e4vak3m25.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18894",
  "fulltext_url": null,
  "id": "38j2e4vak3m25",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18894",
  "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.GM"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7222041282",
  "pdf_url": "https://arxiv.org/pdf/2610.18894",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38j2e4vak3m25.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.18894",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18894"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Algebraic Geometry and Number Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On the nonnegative integer solutions to the equation $F_n^2+F_m=2^{a}$",
  "title_text": "On the nonnegative integer solutions to the equation F_n^2+F_m=2^a",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/38j2e4vak3m25",
  "venue": "arXiv",
  "versions": []
}