{
  "id": "1102.4833",
  "version": "v1",
  "published": "2011-02-22T03:18:42.000Z",
  "updated": "2011-02-22T03:18:42.000Z",
  "title": "The generalized Pillai equation $\\pm r a^x \\pm s b^y = c$, II",
  "authors": [
    "Reese Scott",
    "Robert Styer"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "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 $s>0$. When $(ra,sb)=1$, we show that $N \\le 3$ except for a finite number of cases all of which satisfy $\\max(a,b,r,s, x,y) < 2 \\cdot 10^{15}$ for each solution; when $(a,b)>1$, we show that $N \\le 3$ except for three infinite families of exceptional cases. We find several different ways to generate an infinite number of infinite families of cases giving N=3 solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-22T03:18:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D61"
    ],
    "keywords": [
      "generalized pillai equation",
      "infinite families",
      "exceptional cases",
      "infinite number",
      "nonnegative integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.4833S"
    }
  }
}