{
  "id": "2010.05651",
  "version": "v1",
  "published": "2020-10-12T12:37:48.000Z",
  "updated": "2020-10-12T12:37:48.000Z",
  "title": "On a criterion for Catalan's Conjecture",
  "authors": [
    "Jan-Christoph Schlage-Puchta"
  ],
  "journal": "Ramanujan J. 5 (2001), no. 4, 405-407 (2002)",
  "doi": "10.1023/A:1013947922505",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a new proof of a theorem by P. Mihailescu which states that the equation $x^p-y^q=1$ is unsolvable with $x, y$ integral and $p, q$ odd primes, unless the congruences $p^q \\equiv p\\pmod{q^2}$ and $q^p\\equiv q \\pmod{p^2}$ hold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-12T12:37:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D61"
    ],
    "keywords": [
      "catalans conjecture",
      "odd primes",
      "mihailescu"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}