{
  "id": "2412.04632",
  "version": "v1",
  "published": "2024-12-05T21:53:56.000Z",
  "updated": "2024-12-05T21:53:56.000Z",
  "title": "Smallest totient in a residue class",
  "authors": [
    "Abhishek Jha"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We obtain a totient analogue for Linnik's theorem in arithmetic progressions. Specifically, for any coprime pair of positive integers $(m,a)$ such that $m$ is odd, there exists $n\\le m^{2+o(1)}$ such that $\\varphi(n)\\equiv a\\,\\mathrm{mod}\\,{m}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-05T21:53:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B50",
      "11L40",
      "11N64"
    ],
    "keywords": [
      "residue class",
      "smallest totient",
      "totient analogue",
      "linniks theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}