{
  "id": "0907.0692",
  "version": "v1",
  "published": "2009-07-03T18:39:21.000Z",
  "updated": "2009-07-03T18:39:21.000Z",
  "title": "On the Diophantine equation x^4-q^4=py^5",
  "authors": [
    "Diana Savin"
  ],
  "comment": "This paper was accepted for publication in Italian Journal of Pure and Applied Mathematics",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we study the Diophantine equation $x^{4}-q^{4}=py^{5},$ with the following conditions: $p$ and $q$ are different prime natural numbers, $y$ is not divisible with $p$, $p\\equiv3$ (mod20), $q\\equiv4$ (mod5), $\\overline{p}$ is a generator of the group $(U(\\textbf{Z}_{q^{4}}),\\cdot)$, $(x,y)=1$, 2 is a 5-power residue mod $q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-07-03T18:39:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D41"
    ],
    "keywords": [
      "diophantine equation",
      "prime natural numbers",
      "residue mod",
      "conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.0692S"
    }
  }
}