{
  "id": "1509.08811",
  "version": "v1",
  "published": "2015-09-29T15:40:33.000Z",
  "updated": "2015-09-29T15:40:33.000Z",
  "title": "How to prove this polynomial always has integer values at all integers",
  "authors": [
    "Wilberd van der Kallen"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The following problem was posed by user ``Kevin'' on Mathoverflow. How to prove this polynomial always has integer values at all integers? $$P_m(x)=\\sum_{i=0}^{m}\\sum_{j=0}^{m} \\binom{x+j}{j} \\binom{x-1}{j} \\binom{j}{i} \\binom{m}{i} \\binom{i}{m-j} \\frac{3}{(2i-1)(2j+1)(2m-2i-1)}.$$ We provide an answer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-29T15:40:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B83"
    ],
    "keywords": [
      "integer values",
      "polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}