{
  "id": "2302.04037",
  "version": "v1",
  "published": "2023-02-08T13:19:00.000Z",
  "updated": "2023-02-08T13:19:00.000Z",
  "title": "Prime numbers as a uniqueness set of the parallelogram equation via the Goldbach's conjecture",
  "authors": [
    "Hee Chul Pak",
    "Dongseung Kang"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Multiplicative arithmetic functions satisfying the parallelogram functional equation on prime numbers are investigated. It is derived that the unique non-trivial solution is a quadratic function by the Goldbach's conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-08T13:19:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A25",
      "11A41",
      "11N05",
      "11P32"
    ],
    "keywords": [
      "prime numbers",
      "goldbachs conjecture",
      "uniqueness set",
      "parallelogram equation",
      "unique non-trivial solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}