{
  "id": "1607.01258",
  "version": "v1",
  "published": "2016-07-05T14:21:00.000Z",
  "updated": "2016-07-05T14:21:00.000Z",
  "title": "A variation of a congruence of Subbarao for n=2^(alpha)*5^(beta)",
  "authors": [
    "Sanda Bujačić"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "There are many open problems concerning the characterization of the positive integers $n$ fulfilling certain congruences and involving the Euler totient function $\\varphi$ and the sum of positive divisors function $\\sigma$ of the positive integer $n$. In this work, we deal with the congruence of the form $$ n\\varphi(n)\\equiv2\\pmod{\\sigma(n)} $$ and we prove that the only positive integers of the form $2^{\\alpha}5^{\\beta}, \\enspace \\alpha, \\beta\\geq0,$ that satisfy the above congruence are $n=1, 2, 5, 8$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-05T14:21:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "congruence",
      "positive integer",
      "euler totient function",
      "positive divisors function",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}