{
  "id": "2407.11525",
  "version": "v1",
  "published": "2024-07-16T09:07:24.000Z",
  "updated": "2024-07-16T09:07:24.000Z",
  "title": "On a Theorem of Nathanson on Diophantine Approximation",
  "authors": [
    "Jaroslav Hančl",
    "Tho Phuoc Nguyen"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In 1974, M. B. Nathanson proved that every irrational number $\\alpha$ represented by a simple continued fraction with infinitely many elements greater than or equal to $k$ is approximable by an infinite number of rational numbers $p/q$ satisfying $|\\alpha-p/q|<1/(\\sqrt{k^2+4}q^2)$. In this paper we refine this result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-16T09:07:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J82",
      "11A55"
    ],
    "keywords": [
      "diophantine approximation",
      "simple continued fraction",
      "irrational number",
      "elements greater",
      "infinite number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}