{
  "id": "2108.13471",
  "version": "v1",
  "published": "2021-08-30T18:37:58.000Z",
  "updated": "2021-08-30T18:37:58.000Z",
  "title": "On the 2-adic valuation of (a^b-c^d)",
  "authors": [
    "Luca Onnis"
  ],
  "comment": "15 pages, 9 figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper will be proved an inequality regarding $v_2(a^{b}-c^{d})$. Using this formula it will be possible to have informations about the divisibility of 2 of this function without computing it. Then, will be studied the behavior of this function when it approaches infinity and there will be a lot of analogies with 2-adic integers. This result may be easily used on a calculator, to facilitate the analysis of the divisibility by 2 of this function for large values. Furthermore 2-adic valuation and in general 2-adic analysis is related to binary system, and every work related to it could have a lot of applications in informatics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-30T18:37:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S99"
    ],
    "keywords": [
      "divisibility",
      "approaches infinity",
      "large values",
      "binary system",
      "informations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}