{
  "id": "1703.04950",
  "version": "v1",
  "published": "2017-03-15T06:13:58.000Z",
  "updated": "2017-03-15T06:13:58.000Z",
  "title": "Complete solution of the Diophantine Equation $x^{2}+5^{a}\\cdot 11^{b}=y^{n}$",
  "authors": [
    "Gökhan Soydan",
    "Nikos Tzanakis"
  ],
  "comment": "35 pages",
  "journal": "published in the Bull. Hellenic Math. Soc. 60 (2016), 125-151: http://bulletin.math.uoc.gr/vol/60/60-125-151.pdf",
  "categories": [
    "math.NT"
  ],
  "abstract": "The title equation is completely solved in integers $(n,x,y,a,b)$, where $n\\geq 3$, $\\gcd(x,y)=1$ and $a,b\\geq 0$. The most difficult stage of the resolution is the explicit resolution of a quintic Thue-Mahler equation. Since it is for the first time -to the best of our knowledge- that such an equation is solved in the literature, we make a detailed presentation of the resolution; this gives our paper also an expository character.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-15T06:13:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D61",
      "11D59",
      "11D41",
      "11J86",
      "11Y40"
    ],
    "keywords": [
      "diophantine equation",
      "complete solution",
      "quintic thue-mahler equation",
      "first time",
      "expository character"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}