{
  "id": "1903.01076",
  "version": "v1",
  "published": "2019-03-04T05:21:25.000Z",
  "updated": "2019-03-04T05:21:25.000Z",
  "title": "On the finiteness of solutions for polynomial-factorial Diophantine equations",
  "authors": [
    "Wataru Takeda"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the number of integer solutions $(x,y,l)$ of an equation $F(x,y)=\\Pi_K(l)$, where $F(x,y)$ is a homogeneous polynomial with integer coefficients and $\\Pi_K(l)$ is a generalized factorial function over number fields. We show a necessary condition for the existence of infinitely many solutions. As a corollary, we obtain the finiteness of solution for $P(x)=l!$, where $P$ is decomposed into irreducible polynomials of even degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-04T05:21:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D09",
      "11D45",
      "11D72",
      "11D85"
    ],
    "keywords": [
      "polynomial-factorial diophantine equations",
      "finiteness",
      "integer coefficients",
      "integer solutions",
      "generalized factorial function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}