{
  "id": "1307.5328",
  "version": "v1",
  "published": "2013-07-17T21:22:33.000Z",
  "updated": "2013-07-17T21:22:33.000Z",
  "title": "The Diophantine equation xy=z^n; for n=2,3,4,5,6; the Diophantine equation xyz=w^2; and the Diophantine system: xy=v^2 and yz=w^2",
  "authors": [
    "Konstantine Zelator"
  ],
  "comment": "19 pages, no figures",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this work, we accomplish three goals. First, we determine the entire family of positive integer solutions to the three- variable Diophantine equation, xy=z^2; for n=2,3,4,5,6. For n=2, we obtain a 3-parameter family of solutions; for n=3, a 5-parameter of solutions; likewise for n=4. For n=5, a 7-parameter family of solutions; and likewise for n=6. See Theorems 2 through 6 respectively. The second goal of this paper, is determining all the positive integer solutions of xyz=w^2. This is done in Theorem7; the solution set is described in terms of six independent parameters. Finally, in Theorem 8, we achieve our third goal: determining all the positive integer solutions of the 5-variable Diophantine system: xy=v^2 and yz=w^2. The solution set is expressed in terms of eight parameters. This paper contains a total of four references.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-17T21:22:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diophantine system",
      "positive integer solutions",
      "solution set",
      "paper contains",
      "third goal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.5328Z"
    }
  }
}