{
  "id": "2204.08455",
  "version": "v1",
  "published": "2022-04-18T17:59:19.000Z",
  "updated": "2022-04-18T17:59:19.000Z",
  "title": "On perfect powers that are sum of two balancing numbers",
  "authors": [
    "Pritam Kumar Bhoi",
    "Sudhansu Sekhar Rout",
    "Gopal Krishna Panda"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $B_k$ denote the $k^{th}$ term of balancing sequence. In this paper we find all positive integer solutions of the Diophantine equation $B_n+B_m = x^q$ in variables $(m, n,x,q)$ under the assumption $n\\equiv m \\pmod 2$. Furthermore, we study the Diophantine equation \\[B_n^{3}\\pm B_m^{3} = x^q\\] with positive integer $q\\geq 3$ and $\\gcd(B_n, B_m) =1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-18T17:59:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B37"
    ],
    "keywords": [
      "perfect powers",
      "balancing numbers",
      "diophantine equation",
      "positive integer solutions",
      "balancing sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}