{
  "abstract": "One conjectures that all integers greater than 14 are the sum of an odd prime and two positive squares. We prove that all integers $n$ with $14<n<10^{26}$ can be represented in this manner. Along the way, we investigate sums of a prime and one square and then ``bootstrap'' to get our results on sums of a prime and two squares. We also show that all integers between $308$ and $10^{16}$ can be represented as the sum of an odd prime and two positive cubes. Our methods require the determination of the integral points on various elliptic curves.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20505",
  "author_total": 2,
  "authors": [
    {
      "name": "Kenny Applegate"
    },
    {
      "name": "Kyle Pratt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2bbn2zbxc6zar.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20505",
  "fulltext_url": null,
  "id": "2bbn2zbxc6zar",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20505",
  "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": "W7213608602",
  "pdf_url": "https://arxiv.org/pdf/2609.20505",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2bbn2zbxc6zar.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.20505",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20505"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Computational results on sums of a prime with squares or cubes",
  "title_text": "Computational results on sums of a prime with squares or cubes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/2bbn2zbxc6zar",
  "venue": "arXiv",
  "versions": []
}