{
  "abstract": "We prove that, for $n \\in \\mathbb{Z}^+$ not a perfect square, the only pairs of positive integers $\\{a, b\\}$ for which there exists $r \\in \\mathbb{R}$ such that $r^a + \\sqrt{n}$ and $r^b + \\sqrt{n}$ are both rational numbers are those of the form $\\{a, a\\}$ or $\\{g, 2g\\}$ (with $g$ odd). This resolves an open question presented in the 2023 Simon Marais Mathematics Competition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30658",
  "author_total": 1,
  "authors": [
    {
      "name": "Anthony Pisani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2d5bdxem945y5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30658",
  "fulltext_url": null,
  "id": "2d5bdxem945y5",
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  "landing_url": "https://arxiv.org/abs/2610.30658",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7223320852",
  "pdf_url": "https://arxiv.org/pdf/2610.30658",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2d5bdxem945y5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.30658",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30658"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Open Problem in the 2023 Simon Marais Mathematics Competition",
  "title_text": "On the Open Problem in the 2023 Simon Marais Mathematics Competition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/2d5bdxem945y5",
  "venue": "arXiv",
  "versions": []
}