{
  "id": "1909.12143",
  "version": "v1",
  "published": "2019-09-26T14:27:02.000Z",
  "updated": "2019-09-26T14:27:02.000Z",
  "title": "Zsigmondy's Theorem for Chebyshev polynomials",
  "authors": [
    "Stefan Barańczuk"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For every natural number $a>1$ consider the sequence $(T_{n}(a)-1)_{n=1}^{\\infty}$ defined by Chebyshev polynomials $T_{n}$. We list all pairs $(n,a)$ for which the term $T_{n}(a)-1$ has no primitive prime divisor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-26T14:27:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chebyshev polynomials",
      "zsigmondys theorem",
      "natural number",
      "primitive prime divisor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}