{
  "id": "2310.08422",
  "version": "v1",
  "published": "2023-10-12T15:43:24.000Z",
  "updated": "2023-10-12T15:43:24.000Z",
  "title": "Pell and Pell-Lucas numbers as difference of two repdigits",
  "authors": [
    "Bilizimbeye Edjeou",
    "Bernadette Faye"
  ],
  "comment": "to appear in Afrika Matematika",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $ \\{P_{n}\\}_{n\\geq 0} $ be the sequence of Pell numbers defined by $ P_0=0 $, $ P_1 =1$ and $ P_{n+2}= 2P_{n+1} +P_n$ for all $ n\\geq 0 $ and let $ \\{Q_{n}\\}_{n\\geq 0} $ be its companion sequence, the Pell-Lucas numbers defined by $ Q_0=Q_1 =2$ and $ Q_{n+2}= 2Q_{n+1} +Q_n$ for all $ n\\geq 0 $ . In this paper, we find all Pell and Pell-Lucas numbers which can be written as difference of two repdigits. It is shown that the largest Pell and Pell-Lucas numbers which can be written as difference of two repdigits are $$P_6=70= 77-7 \\quad\\quad \\hbox{and} \\quad\\quad Q_7 = 478=555-77.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-12T15:43:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pell-lucas numbers",
      "difference",
      "largest pell"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}