{
  "id": "1607.06681",
  "version": "v1",
  "published": "2016-07-22T13:50:13.000Z",
  "updated": "2016-07-22T13:50:13.000Z",
  "title": "Sum of two repdigits a square",
  "authors": [
    "Bart Goddard",
    "Jeremy Rouse"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "A \\emph{repdigit} is a natural number greater than 10 which has all of its base-10 digits the same. In this paper we find all examples of two repdigits adding to a square. The proofs lead to interesting questions about consecutive quadratic residues and non-residues, and provide an elementary application of elliptic curves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-22T13:50:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D61",
      "11G05",
      "11A63"
    ],
    "keywords": [
      "natural number greater",
      "consecutive quadratic residues",
      "elementary application",
      "elliptic curves",
      "non-residues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}