{
  "id": "2109.11883",
  "version": "v2",
  "published": "2021-09-24T11:01:24.000Z",
  "updated": "2023-11-24T14:15:38.000Z",
  "title": "On the sum of a prime and a square-free number with divisibility conditions",
  "authors": [
    "Shehzad Hathi",
    "Daniel R. Johnston"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Every integer greater than two can be expressed as the sum of a prime and a square-free number. Expanding on recent work, we provide explicit and asymptotic results when divisibility conditions are imposed on the square-free number. For example, we show for odd $k\\leq 10^5$ and even $k\\leq 2\\cdot 10^5$ that any even integer $n\\geq 40$ can be expressed as the sum of a prime and a squarefree number coprime to $k$. We also discuss applications to other Goldbach-like problems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-11-24T14:15:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P32",
      "11Y99"
    ],
    "keywords": [
      "square-free number",
      "divisibility conditions",
      "squarefree number coprime",
      "asymptotic results",
      "integer greater"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}