{
  "id": "1602.08698",
  "version": "v1",
  "published": "2016-02-28T10:39:52.000Z",
  "updated": "2016-02-28T10:39:52.000Z",
  "title": "Equal Sums of Like Powers with Minimum Number of Terms",
  "authors": [
    "Ajai Choudhry"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper is concerned with the diophantine system, $\\sum_{i=1}^{s_1} x_i^r=\\sum_{i=1}^{s_2} y_i^r,\\, r=1,\\,2,\\,\\ldots,\\,k, $ where $s_1$ and $s_2$ are integers such that the total number of terms on both sides, that is, $s_1+s_2,$ is as small as possible. We define $\\beta(k)$ to be the minimum value of $s_1+s_2$ for which there exists a nontrivial solution of this diophantine system. We find nontrivial integer solutions of this diophantine system when $k < 6$, and thereby show that $\\beta(2) =4,\\;\\, \\beta(3) = 6,\\;\\, 7 \\leq \\beta(4) \\leq 8$ and $8 \\leq \\beta(5) \\leq 10$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-28T10:39:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D25",
      "11D41"
    ],
    "keywords": [
      "equal sums",
      "minimum number",
      "diophantine system",
      "nontrivial integer solutions",
      "nontrivial solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}