{
  "id": "2303.06534",
  "version": "v1",
  "published": "2023-03-12T01:30:53.000Z",
  "updated": "2023-03-12T01:30:53.000Z",
  "title": "Every arithmetic progression contains infinitely many $b$-Niven numbers",
  "authors": [
    "Joshua Harrington",
    "Matthew Litman",
    "Tony W. H. Wong"
  ],
  "journal": "Bull. Aust. Math. Soc. 109 (2024) 409-413",
  "doi": "10.1017/S0004972723000758",
  "categories": [
    "math.NT"
  ],
  "abstract": "For an integer $b\\geq 2$, a positive integer is called a $b$-Niven number if it is a multiple of the sum of the digits in its base-$b$ representation. In this article, we show that every arithmetic progression contains infinitely many $b$-Niven numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-12T01:30:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A63",
      "11B25"
    ],
    "keywords": [
      "arithmetic progression contains",
      "niven number",
      "representation",
      "positive integer"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}