{
  "id": "2404.03970",
  "version": "v1",
  "published": "2024-04-05T09:08:59.000Z",
  "updated": "2024-04-05T09:08:59.000Z",
  "title": "A question of Erdös on $3$-powerful numbers and an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture",
  "authors": [
    "P. G. Walsh"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We describe how the Mordell-Weil group of rational points on a certain family of elliptic curves give rise to solutions to a conjecture of Erd\\\"{o}s on $3$-powerful numbers, and state a related conjecture which can be viewed as an elliptic curve analogue of the Ankeny-Artin-Chowla conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-05T09:08:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D25"
    ],
    "keywords": [
      "elliptic curve analogue",
      "ankeny-artin-chowla conjecture",
      "powerful numbers",
      "rational points",
      "mordell-weil group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}