{
  "id": "1907.05266",
  "version": "v1",
  "published": "2019-07-10T16:24:41.000Z",
  "updated": "2019-07-10T16:24:41.000Z",
  "title": "New families of strong Skolem starters",
  "authors": [
    "Adrián Vázquez-Ávila"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1901.07514",
  "categories": [
    "math.CO"
  ],
  "abstract": "In 1991, N. Shalaby conjectured that any additive group $\\mathbb{Z}_n$, where $n\\equiv1$ or 3 (mod 8) and $n \\geq11$, admits a strong Skolem starter and constructed these starters of all admissible orders $11\\leq n\\leq57$. Recently, N. Shalaby and et al. [O. Ogandzhanyants, M. Kondratieva and N. Shalaby, \\emph{Strong Skolem Starters}, J. Combin. Des. {\\bf 27} (2018), no. 1, 5--21] was proved if $n=\\Pi_{i=1}^{k}p_i^{\\alpha_i}$, where $p_i$ is a prime such that $ord(2)_{p_i}\\equiv 2$ (mod 4) and $\\alpha_i$ is a non-negative integer, for all $i=1,\\ldots,k$, then $\\mathbb{Z}_n$ admits a strong Skolem starter, where $ord(2)_{p_i}$ means the order of the element 2 in $\\mathbb{Z}_{p_i}$. On the other hand, the author proved [A. V\\'azquez-\\'Avila, \\emph{A note on strong Skolem starters}, Discrete Math. Accepted] if $p\\equiv3$ (mod 8) is an odd prime, then $\\mathbb{Z}_p$ admits a strong Skolem starter. In this paper, we prove that, if $p\\equiv3$ (mod 8) and $n$ is an integer greater than 1, then $\\mathbb{Z}_{p^n}$ admits a strong Skolem starter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-10T16:24:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strong skolem starter",
      "discrete math",
      "odd prime",
      "integer greater",
      "additive group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}