{
  "id": "2401.01293",
  "version": "v1",
  "published": "2024-01-02T17:10:16.000Z",
  "updated": "2024-01-02T17:10:16.000Z",
  "title": "Bounds on the number of squares in recurrence sequences",
  "authors": [
    "Paul M Voutier"
  ],
  "comment": "Submitted version. Comments welcome",
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the number of squares in a very broad family of binary recurrence sequences with $u_{0}=1$. We show that there are at most two distinct squares in such sequences (the best possible result), except under such very special conditions where we prove there are at most three such squares.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-02T17:10:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B37",
      "11B39",
      "11J82"
    ],
    "keywords": [
      "binary recurrence sequences",
      "distinct squares",
      "special conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}