{
  "id": "1006.1196",
  "version": "v1",
  "published": "2010-06-07T08:04:47.000Z",
  "updated": "2010-06-07T08:04:47.000Z",
  "title": "The Diophantine Equation $x^4 + 2 y^4 = z^4 + 4 w^4$---a number of improvements",
  "authors": [
    "Andreas-Stephan Elsenhans",
    "Jörg Jahnel"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "The quadruple $(1\\,484\\,801, 1\\,203\\,120, 1\\,169\\,407, 1\\,157\\,520)$ already known is essentially the only non-trivial solution of the Diophantine equation $x^4 + 2 y^4 = z^4 + 4 w^4$ for $|x|$, $|y|$, $|z|$, and $|w|$ up to one hundred million. We describe the algorithm we used in order to establish this result, thereby explaining a number of improvements to our original approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-06-07T08:04:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11Y50",
      "14G05",
      "14J28"
    ],
    "keywords": [
      "diophantine equation",
      "improvements",
      "non-trivial solution",
      "original approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.1196E"
    }
  }
}