{
  "id": "2101.07593",
  "version": "v1",
  "published": "2021-01-19T12:34:57.000Z",
  "updated": "2021-01-19T12:34:57.000Z",
  "title": "Additive bases and Niven numbers",
  "authors": [
    "Carlo Sanna"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $g \\geq 2$ be an integer. A natural number is said to be a base-$g$ Niven number if it is divisible by the sum of its base-$g$ digits. Assuming Hooley's Riemann Hypothesis for $g$, we prove that the set of base-$g$ Niven numbers is an additive basis, that is, there exists $C_g > 0$ such that every natural number is the sum of at most $C_g$ base-$g$ Niven numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-19T12:34:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B13",
      "11A63"
    ],
    "keywords": [
      "niven number",
      "additive basis",
      "natural number",
      "assuming hooleys riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}