{
  "id": "1908.01690",
  "version": "v1",
  "published": "2019-08-05T15:25:44.000Z",
  "updated": "2019-08-05T15:25:44.000Z",
  "title": "Explicit Formulas for the p-adic Valuations of Fibonomial Coefficients II",
  "authors": [
    "Phakhinkon Phunphayap",
    "Prapanpong Pongsriiam"
  ],
  "comment": "updated and submitted",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this article, we give explicit formulas for the $p$-adic valuations of the Fibonomial coefficients ${p^a n \\choose n}_F$ for all primes $p$ and positive integers $a$ and $n$. This is a continuation from our previous article extending some results in the literature, which deal only with $p = 2,3,5,7$ and $a = 1$. Then we use these formulas to characterize the positive integers $n$ such that ${pn \\choose n}_F$ is divisible by $p$, where $p$ is any prime which is congruent to $\\pm 2 \\pmod{5}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-05T15:25:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11B65",
      "11A63"
    ],
    "keywords": [
      "explicit formulas",
      "fibonomial coefficients",
      "p-adic valuations",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}