{
  "id": "2505.02528",
  "version": "v1",
  "published": "2025-05-05T10:09:31.000Z",
  "updated": "2025-05-05T10:09:31.000Z",
  "title": "Magic squares on Abelian groups",
  "authors": [
    "Sylwia Cichacz",
    "Dalibor Froncek"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $(\\Gamma,+)$ be an Abelian group of order $n^2$ and MS$_{\\Gamma}(n)$ be an $n\\times n$ array whose entries are all elements of $\\Gamma$. Then MS$_{\\Gamma}(n)$ is a $\\Gamma$-magic square if all row, column, main and backward main diagonal sums are equal to the same element $\\mu\\in\\Gamma$. We prove that for every Abelian group $\\Gamma$ of order $n^2$, $n>2$, there exists a magic square MS$_{\\Gamma}(n)$ where the square entries are elements of $\\Gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-05T10:09:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15"
    ],
    "keywords": [
      "abelian group",
      "magic square ms",
      "backward main diagonal sums",
      "square entries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}