{
  "id": "1501.01843",
  "version": "v1",
  "published": "2015-01-08T13:46:43.000Z",
  "updated": "2015-01-08T13:46:43.000Z",
  "title": "On the coefficients of power sums of arithmetic progressions",
  "authors": [
    "András Bazsó",
    "István Mező"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the coefficients of the polynomial \\[ S_{m,r}^n(\\ell)=r^n+(m+r)^n+(2m+r)^n+\\cdots+((\\ell-1)m+r)^n. \\] We prove that these can be given in terms of Stirling numbers of the first kind and $r$-Whitney numbers of the second kind. Moreover, we prove a necessary and sufficient condition for the integrity of these coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-08T13:46:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B25",
      "11B68",
      "11B73"
    ],
    "keywords": [
      "arithmetic progressions",
      "power sums",
      "coefficients",
      "sufficient condition",
      "first kind"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}