{
  "id": "1209.5706",
  "version": "v1",
  "published": "2012-09-25T18:05:06.000Z",
  "updated": "2012-09-25T18:05:06.000Z",
  "title": "A note on rational and elliptic curves associated with the cuboid factor equations",
  "authors": [
    "Ruslan Sharipov"
  ],
  "comment": "AmSTeX, 15 pages, amsppt style, 1 ancillary file. arXiv admin note: substantial text overlap with arXiv:1209.0723",
  "categories": [
    "math.NT"
  ],
  "abstract": "A rational perfect cuboid is a rectangular parallelepiped whose edges and face diagonals are given by rational numbers and whose space diagonal is equal to unity. It is described by a system of four equations with respect to six variables. The cuboid factor equations were derived from these four equations by symmetrization procedure. They constitute a system of eight polynomial equations, which has been solved parametrically. In the present paper its parametric solution is expressed through intersections or rational and elliptic curves arranged into parametric families.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-25T18:05:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D25",
      "11D72",
      "14E05",
      "14H45",
      "14H52"
    ],
    "keywords": [
      "cuboid factor equations",
      "elliptic curves",
      "rational perfect cuboid",
      "face diagonals",
      "rational numbers"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.5706S"
    }
  }
}