{
  "id": "1102.4834",
  "version": "v1",
  "published": "2011-02-22T03:45:07.000Z",
  "updated": "2011-02-22T03:45:07.000Z",
  "title": "The generalized Pillai equation $\\pm r a^x \\pm s b^y = c$",
  "authors": [
    "Reese Scott",
    "Robert Styer"
  ],
  "comment": "This is an updated version (expanding the comment on values of exponents = 0) of the paper published in Journal of Number Theory, June 2011",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we consider $N$, the number of solutions $(x,y,u,v)$ to the equation $ (-1)^u r a^x + (-1)^v s b^y = c$ in nonnegative integers $x, y$ and integers $u, v \\in \\{0,1\\}$, for given integers $a>1$, $b>1$, $c>0$, $r>0$ and $s>0$. We show that $N \\le 2$ when $\\gcd(ra, sb) =1$ and $\\min(x,y)>0$, except for a finite number of cases that can be found in a finite number of steps. For arbitrary $\\gcd(ra, sb)$ and $\\min(x,y) \\ge 0$, we show that when $(u,v) = (0,1)$ we have $N \\le 3$, with an infinite number of cases for which N=3.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-22T03:45:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D61"
    ],
    "keywords": [
      "generalized pillai equation",
      "infinite number",
      "nonnegative integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.4834S"
    }
  }
}