{
  "id": "2202.02100",
  "version": "v1",
  "published": "2022-02-04T12:20:57.000Z",
  "updated": "2022-02-04T12:20:57.000Z",
  "title": "A Divisor problem for polynomials",
  "authors": [
    "Benjamin Klahn"
  ],
  "comment": "Acta Arithmetica 200 (2021), 111-118",
  "doi": "10.4064/aa200528-21-4",
  "categories": [
    "math.NT"
  ],
  "abstract": "We characterize all monic polynomials $f(x) \\in \\mathbb{Z}[x]$ that have the property that \\[f(p) \\mid f(p^{p}),~\\text{for all sufficiently large primes }p \\geq N(f). \\] We also give necessary conditions and a sufficient condition for monic polynomials $f(x) \\in \\mathbb{Z}[x]$ to satisfy $f(p) \\mid f(p^{p})$ for all primes $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-04T12:20:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11C08",
      "11T06"
    ],
    "keywords": [
      "divisor problem",
      "monic polynomials",
      "sufficiently large primes",
      "necessary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}