{
  "id": "2407.11166",
  "version": "v1",
  "published": "2024-07-15T18:38:31.000Z",
  "updated": "2024-07-15T18:38:31.000Z",
  "title": "On a Theorem of Legendre on Diophantine Approximation",
  "authors": [
    "Jaroslav Hančl",
    "Tho Phuoc Nguyen"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Legendre's theorem states that every irreducible fraction $\\frac{p}{q}$ which satisfies the inequality $\\left |\\alpha-\\frac{p}{q} \\right | < \\frac{1}{2q^2}$ is convergent to $\\alpha$. Later Barbolosi and Jager improved this theorem. In this paper we refine these results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-15T18:38:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J82",
      "11A55"
    ],
    "keywords": [
      "diophantine approximation",
      "legendres theorem states",
      "inequality",
      "convergent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}