{
  "id": "2008.12506",
  "version": "v1",
  "published": "2020-08-28T06:59:48.000Z",
  "updated": "2020-08-28T06:59:48.000Z",
  "title": "On the divisibility of the rank of appearance of a Lucas sequence",
  "authors": [
    "Carlo Sanna"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $U = (U_n)_{n \\geq 0}$ be a Lucas sequence and, for every prime number $p$, let $\\rho_U(p)$ be the rank of appearance of $p$ in $U$, that is, the smallest positive integer $k$ such that $p$ divides $U_k$, whenever it exists. Furthermore, let $d$ be an odd positive integer. Under some mild hypotheses, we prove an asymptotic formula for the number of primes $p \\leq x$ such that $d$ divides $\\rho_U(p)$, as $x \\to +\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-28T06:59:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11N05",
      "11N37"
    ],
    "keywords": [
      "lucas sequence",
      "appearance",
      "divisibility",
      "prime number",
      "smallest positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}