{
  "id": "1601.04886",
  "version": "v1",
  "published": "2016-01-19T12:12:21.000Z",
  "updated": "2016-01-19T12:12:21.000Z",
  "title": "On the $P_1$ property of sequences of positive integers",
  "authors": [
    "Tigran Hakobyan"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "It is well-known that for any non-constant polynomial $P$ with integer coefficients the sequence $(P(n))_{ n\\in \\mathbb N}$ has the property that there are infinitely many prime numbers dividing at least one term of this sequence. Certainly, there is a proof based on the Chinese Remainder Theorem. In this paper we give proofs of two analytic criteria revealing this property of sequences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-19T12:12:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive integers",
      "chinese remainder theorem",
      "non-constant polynomial",
      "analytic criteria",
      "integer coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160104886H"
    }
  }
}