{
  "id": "1705.02597",
  "version": "v1",
  "published": "2017-05-07T11:09:28.000Z",
  "updated": "2017-05-07T11:09:28.000Z",
  "title": "Perfect powers in alternating sum of consecutive cubes",
  "authors": [
    "Pranabesh Das",
    "Pallab Kanti Dey",
    "B. Maji",
    "S. S. Rout"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Recently, Bennett et al. found all perfect powers in the sum of $d$ consecutive cubes with $2 \\leq d \\leq 50$. In this paper, we consider the problem about finding out perfect powers in alternating sum of consecutive cubes. More precisely, we completely solve the Diophantine equation $(x+1)^3 - (x+2)^3 + \\cdots - (x + 2d)^3 + (x + 2d + 1)^3 = z^p$, where $p$ is prime and $x,d,z$ are integers with $1 \\leq d \\leq 50$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-07T11:09:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perfect powers",
      "consecutive cubes",
      "alternating sum",
      "diophantine equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}