{
  "id": "0909.2598",
  "version": "v1",
  "published": "2009-09-14T17:06:16.000Z",
  "updated": "2009-09-14T17:06:16.000Z",
  "title": "The divisibility of a^n-b^n by powers of n",
  "authors": [
    "Chris Smyth"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For given integers a,b, and j at least 1 we determine the set of integers n for which a^n-b^n is divisible by n^j. For j=1,2, this set is usually infinite; we find explicitly the exceptional cases for which a,b the set is finite. For j=2, we use Zsigmondy's Theorem for this. For j at least 3 and gcd(a,b)=1, the set is probably always finite; this seems difficult to prove, however. We also show that determination of the set of integers n for which a^n+b^n is divisible by n^j can be reduced to that of the above set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-14T17:06:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B37",
      "11D61"
    ],
    "keywords": [
      "divisibility",
      "exceptional cases",
      "zsigmondys theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.2598S"
    }
  }
}