{
  "id": "2201.00501",
  "version": "v2",
  "published": "2022-01-03T07:29:02.000Z",
  "updated": "2023-12-11T15:00:03.000Z",
  "title": "A note on the squares of the form $\\prod_{k=1}^n (2k^2+l)$ with $l$ odd",
  "authors": [
    "Russelle Guadalupe"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $l$ be a positive odd integer. Using Cilleruelo's method, we establish an explicit lower bound $N_l$ depending on $l$ such that for all $n\\geq N_l$, $\\prod_{k=1}^n (2k^2+l)$ is not a square. As an application, we determine all values of $n$ such that $\\prod_{k=1}^n (2k^2+l)$ is a square for certain values of $l$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-12-11T15:00:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D09",
      "11C08",
      "11A15"
    ],
    "keywords": [
      "explicit lower bound",
      "cilleruelos method",
      "positive odd integer",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}