{
  "id": "2504.19392",
  "version": "v3",
  "published": "2025-04-27T23:49:57.000Z",
  "updated": "2025-05-07T22:26:43.000Z",
  "title": "A solution to a Paul Erdos problem",
  "authors": [
    "Vyacheslav M. Abramov"
  ],
  "comment": "Dear readers, I need to withdraw this paper since I was shown a counterexample. At this moment I cannot fix an error. I shall return to this question as soon as I find a solution",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Paul Erdos posed the following question: Is there a prime number $p>5$ such that the residues of $2!$, $3!$,\\ldots, $(p-1)!$ modulo $p$ all are distinct? In this short note, we prove that there are no such prime numbers.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2025-05-07T22:26:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A41",
      "11A07",
      "05A05",
      "05A10"
    ],
    "keywords": [
      "paul erdos problem",
      "prime number",
      "short note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}