{
  "abstract": "We prove that for any $s\\ge 2$ and polynomials $f_{1}(x),\\dots,f_{s-1}(x)\\in \\mathbb{R}[x]$ satisfying a certain equidistribution condition, the natural density of the numbers $n\\in \\mathbb{N}$ such that $n,\\lfloor f_{1}(n)\\rfloor,\\dots,\\lfloor f_{s-1}(n)\\rfloor$ are mutually coprime is $1/ζ(s)$. This generalises a recent result of Champagne, in which this was proven under the assumption that $f_{1}$ is linear.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02223",
  "author_total": 1,
  "authors": [
    {
      "name": "Philippa Holdridge"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/08be5g7jc1v3y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02223",
  "fulltext_url": null,
  "id": "08be5g7jc1v3y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02223",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02223",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/08be5g7jc1v3y.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02223",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02223"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the probability that the integer parts of polynomials are coprime",
  "title_text": "On the probability that the integer parts of polynomials are coprime",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/08be5g7jc1v3y",
  "venue": "arXiv",
  "versions": []
}