{
  "id": "1302.5708",
  "version": "v1",
  "published": "2013-02-22T21:02:55.000Z",
  "updated": "2013-02-22T21:02:55.000Z",
  "title": "An Unexpected Congruence Modulo 5 for 4--Colored Generalized Frobenius Partitions",
  "authors": [
    "James A. Sellers"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In his 1984 AMS Memoir, George Andrews defined the family of $k$--colored generalized Frobenius partition functions. These are denoted by $c\\phi_k(n)$ where $k\\geq 1$ is the number of colors in question. In that Memoir, Andrews proved (among many other things) that, for all $n\\geq 0,$ $c\\phi_2(5n+3) \\equiv 0\\pmod{5}.$ Soon after, many authors proved congruence properties for various $k$--colored generalized Frobenius partition functions, typically with a small number of colors. In 2011, Baruah and Sarmah proved a number of congruence properties for $c\\phi_4$, all with moduli which are powers of 4. In this brief note, we add to the collection of congruences for $c\\phi_4$ by proving this function satisfies an unexpected result modulo 5. The proof is elementary, relying on Baruah and Sarmah's results as well as work of Srinivasa Ramanujan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-22T21:02:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "unexpected congruence modulo",
      "colored generalized frobenius partition functions",
      "congruence properties",
      "brief note",
      "george andrews"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.5708S"
    }
  }
}