{
  "id": "2107.12121",
  "version": "v1",
  "published": "2021-07-26T11:38:18.000Z",
  "updated": "2021-07-26T11:38:18.000Z",
  "title": "On some symmetries of the base $ n $ expansion of $ 1/m $ : Comments on Artin's Primitive root conjecture",
  "authors": [
    "Kalyan Chakraborty",
    "Krishnarjun Krishnamoorthy"
  ],
  "comment": "Eight pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Suppose $ m,n\\geq 2 $ are co prime integers. We prove certain new symmetries of the base $ n $ representation of $ 1/m $, and in particular characterize the subgroup generated by $ n $ inside $ (\\mathbb{Z}/m\\mathbb{Z})^\\times $. As an application we give a sufficient condition for a prime $ p $ such that a non square number $ n $ is a primitive root modulo $ p $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-26T11:38:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07"
    ],
    "keywords": [
      "artins primitive root conjecture",
      "symmetries",
      "non square number",
      "prime integers",
      "primitive root modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}