{
  "id": "1711.08313",
  "version": "v1",
  "published": "2017-11-16T05:03:42.000Z",
  "updated": "2017-11-16T05:03:42.000Z",
  "title": "On the Lehmer's problem involving Euler's totient function",
  "authors": [
    "Huan Xiao"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The Euler's totient function $ \\varphi(n) $ counts the positive integers up to a given integer $ n$ that are relatively prime to $ n $. We solve a problem due to Lehmer that there is no composite number $ n $ such that $ \\varphi(n)\\mid n-1 $. We also note that there are infinitely many primes that are not Sophie Germain primes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-16T05:03:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25"
    ],
    "keywords": [
      "eulers totient function",
      "lehmers problem",
      "sophie germain primes",
      "composite number",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}