{
  "id": "2409.07895",
  "version": "v1",
  "published": "2024-09-12T10:00:58.000Z",
  "updated": "2024-09-12T10:00:58.000Z",
  "title": "Universal sums of generalized polygonal numbers of almost prime \"length\"",
  "authors": [
    "Soumyarup Banerjee",
    "Ben Kane",
    "Daejun Kim"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we consider sums of three generalized $m$-gonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restrictions on $m$ modulo $30$, we show that a density one set of integers is represented as such a sum, where the parameters are restricted to have at most 6361 prime factors. Moreover, if the squarefree part of $f_m(n)$ is sufficiently large, then $n$ is represented as such a sum, where $f_m(n)$ is a natural linear function in $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-12T10:00:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F27",
      "11F37",
      "11E20",
      "11E45",
      "11N36"
    ],
    "keywords": [
      "generalized polygonal numbers",
      "universal sums",
      "natural linear function",
      "prime divisors",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}