{
  "id": "2411.12009",
  "version": "v1",
  "published": "2024-11-18T19:49:15.000Z",
  "updated": "2024-11-18T19:49:15.000Z",
  "title": "More on consecutive multiplicatively dependent triples of integers",
  "authors": [
    "Michael A. Bennett",
    "István Pink",
    "Ingrid Vukusic"
  ],
  "comment": "31 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we extend recent work of the third author and Ziegler on triples of integers $(a,b,c)$, with the property that each of $(a,b,c)$, $(a+1,b+1,c+1)$ and $(a+2,b+2,c+2)$ is multiplicatively dependent, completely classifying such triples in case $a=2$. Our techniques include a variety of elementary arguments together with more involved machinery from Diophantine approximation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-18T19:49:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N25",
      "11D61",
      "11J86"
    ],
    "keywords": [
      "consecutive multiplicatively dependent triples",
      "third author",
      "diophantine approximation",
      "elementary arguments",
      "techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}