{
  "id": "1112.3820",
  "version": "v5",
  "published": "2011-12-16T14:30:43.000Z",
  "updated": "2014-07-17T21:05:36.000Z",
  "title": "Square-free values of f(p), f cubic",
  "authors": [
    "H. A. Helfgott"
  ],
  "comment": "24 pages. Minimal changes",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let f\\in Z[x], deg(f)=3. Assume that f does not have repeated roots. Assume as well that, for every prime q, the inequality f(x)\\not\\equiv 0 mod q^2 has at least one solution in (Z/q^2 Z)^*. Then, under these two necessary conditions, there are infinitely many primes p such that f(p) is square-free.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2014-07-17T21:05:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N32",
      "11D25",
      "11K38"
    ],
    "keywords": [
      "square-free values",
      "necessary conditions",
      "inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.3820H"
    }
  }
}