{
  "id": "1001.4170",
  "version": "v1",
  "published": "2010-01-23T16:33:45.000Z",
  "updated": "2010-01-23T16:33:45.000Z",
  "title": "The sum of digits of $n$ and $n^2$",
  "authors": [
    "K. G. Hare",
    "S. Laishram",
    "T. Stoll"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $s_q(n)$ denote the sum of the digits in the $q$-ary expansion of an integer $n$. In 2005, Melfi examined the structure of $n$ such that $s_2(n) = s_2(n^2)$. We extend this study to the more general case of generic $q$ and polynomials $p(n)$, and obtain, in particular, a refinement of Melfi's result. We also give a more detailed analysis of the special case $p(n) = n^2$, looking at the subsets of $n$ where $s_q(n) = s_q(n^2) = k$ for fixed $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-23T16:33:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "special case",
      "melfis result",
      "ary expansion",
      "general case",
      "refinement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}