{
  "id": "1802.07485",
  "version": "v1",
  "published": "2018-02-21T09:56:49.000Z",
  "updated": "2018-02-21T09:56:49.000Z",
  "title": "Perfect powers that are sums of squares in a three term arithmetic progression",
  "authors": [
    "Angelos Koutsianas",
    "Vandita Patel"
  ],
  "comment": "6 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We determine primitive solutions to the equation $(x-r)^2 + x^2 + (x+r)^2 = y^n$ for $1 \\le r \\le 5,000$, making use of a factorization argument and the Primitive Divisors Theorem due to Bilu, Hanrot and Voutier.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-21T09:56:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "term arithmetic progression",
      "perfect powers",
      "determine primitive solutions",
      "factorization argument",
      "primitive divisors theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}