{
  "id": "1008.5239",
  "version": "v1",
  "published": "2010-08-31T07:44:43.000Z",
  "updated": "2010-08-31T07:44:43.000Z",
  "title": "An analogue of Ramanujan's sum with respect to regular integers (mod $r$)",
  "authors": [
    "Pentti Haukkanen",
    "László Tóth"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "An integer $a$ is said to be regular (mod $r$) if there exists an integer $x$ such that $a^2x\\equiv a\\pmod{r}$. In this paper we introduce an analogue of Ramanujan's sum with respect to regular integers (mod $r$) and show that this analogue possesses properties similar to those of the usual Ramanujan's sum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-31T07:44:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11L03"
    ],
    "keywords": [
      "regular integers",
      "analogue possesses properties similar",
      "usual ramanujans sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.5239H"
    }
  }
}