{
  "id": "2212.11356",
  "version": "v1",
  "published": "2022-12-21T20:48:32.000Z",
  "updated": "2022-12-21T20:48:32.000Z",
  "title": "Parity of 4-regular and 8-regular partition functions",
  "authors": [
    "Giacomo Cherubini",
    "Pietro Mercuri"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a complete characterization of the parity of $b_8(n)$, the number of $8$-regular partitions of $n$. Namely, we prove that $b_8(n)$ is odd or even depending on whether or not we have the factorisation $24n+7=p^{4a+1}m^2$, for some prime $p\\nmid m$ and $a\\ge 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-21T20:48:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P83",
      "11F20"
    ],
    "keywords": [
      "partition functions",
      "complete characterization",
      "regular partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}