{
  "id": "2305.07657",
  "version": "v1",
  "published": "2023-04-09T03:32:49.000Z",
  "updated": "2023-04-09T03:32:49.000Z",
  "title": "Two pairs of biquadrates with equal sums",
  "authors": [
    "Ajai Choudhry"
  ],
  "comment": "4 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we present a new method of solving the classical diophantine equation $A^4+B^4=C^4+D^4$. Two methods of solving this equation, given by Euler, yield parametric solutions given by polynomials of degrees 7 and 13. Several other parametric solutions are now known, and with the exception of one solution of degree 11, all the published solutions are of degrees $6n+1$ for some integer $n$. The method described in this paper yields new parametric solutions of degrees 21, 39 and 75, that is, degrees that are expressible as $6n+3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-09T03:32:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D25"
    ],
    "keywords": [
      "equal sums",
      "biquadrates",
      "yield parametric solutions",
      "classical diophantine equation",
      "paper yields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}