{
  "id": "2204.08971",
  "version": "v1",
  "published": "2022-04-19T16:16:54.000Z",
  "updated": "2022-04-19T16:16:54.000Z",
  "title": "Prime factors of $Φ_3(x)$ of the same form",
  "authors": [
    "Cody S. Hansen",
    "Pace P. Nielsen"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We parameterize solutions to the equality $\\Phi_3(x)=\\Phi_3(a_1)\\Phi_3(a_2)\\cdots\\Phi_3(a_n)$ when each $\\Phi_3(a_i)$ is prime. Our focus is on the special cases when $n=2,3,4$, as this analysis simplifies and extends bounds on the total number of prime factors of an odd perfect number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-19T16:16:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "prime factors",
      "odd perfect number",
      "total number",
      "extends bounds",
      "special cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}