{
  "id": "2104.12680",
  "version": "v1",
  "published": "2021-04-26T16:12:33.000Z",
  "updated": "2021-04-26T16:12:33.000Z",
  "title": "On the exponential Diophantine equation $x^2+5^a13^b17^c=2^m y^n$",
  "authors": [
    "Azizul Hoque"
  ],
  "comment": "Diophantine equation, Lehmer number, Elliptic curve, Quartic curve, S-Integral Points",
  "categories": [
    "math.NT"
  ],
  "abstract": "We find all the positive integer solutions $(x,y,a,b,c,m,n)$ of the Diophantine equation in the title for $a,b,c, m\\geq 0$ and $n \\geq 3$ with $\\gcd(x,y)=1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-26T16:12:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D61",
      "11D41",
      "11Y50"
    ],
    "keywords": [
      "exponential diophantine equation",
      "positive integer solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}