{
  "id": "2302.07368",
  "version": "v1",
  "published": "2023-02-14T22:04:20.000Z",
  "updated": "2023-02-14T22:04:20.000Z",
  "title": "A new characterization of prime numbers and solution to Lehmer's conjecture on Euler's totient function",
  "authors": [
    "Said Zriaa"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "By using the elementary symmetric polynomials and some results of number theory, we solve the well known problem of Lehmer on Euler's totient function. As application, we obtain a new characterization of prime numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-14T22:04:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eulers totient function",
      "prime numbers",
      "lehmers conjecture",
      "characterization",
      "elementary symmetric polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}