{
  "id": "1706.03185",
  "version": "v1",
  "published": "2017-06-10T05:58:45.000Z",
  "updated": "2017-06-10T05:58:45.000Z",
  "title": "A note on the Diophantine equations $x^{2}\\pm5^α\\cdot p^{n}=y^{n}$",
  "authors": [
    "Gökhan Soydan"
  ],
  "comment": "8 pages, accepted for publication in Commun. Fac. Sci. Univ. Ank. Series A1: Math. and Stat",
  "categories": [
    "math.NT"
  ],
  "abstract": "Suppose that $x$ is odd, $n\\geq7$ and $p\\notin\\{2,5\\}$ are primes. In this paper, we prove that the Diophantine equations $x^{2}\\pm5^{\\alpha}p^{n}=y^{n}$ have no solutions in positive integers $\\alpha,x,y$ with $gcd(x,y)=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-10T05:58:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D61"
    ],
    "keywords": [
      "diophantine equations",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}