{
  "id": "2002.07043",
  "version": "v1",
  "published": "2020-02-17T16:35:25.000Z",
  "updated": "2020-02-17T16:35:25.000Z",
  "title": "Necessary conditions for binomial collisions",
  "authors": [
    "Tomohiro Yamada"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We shall give some necessary conditions for the equation $\\binom{x}{a}=\\binom{y}{b}$ to hold: if $\\binom{2n+\\delta}{n-m}=\\binom{2n+l}{n-k}$ with $\\delta=0$ or $1$, $0<m\\leq 0.735k$, $k<n$ and $n$ sufficiently large, then $l>(cn/\\log n)^{40/21}$ for some constant $c$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-17T16:35:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "11A05",
      "11D61",
      "11D72"
    ],
    "keywords": [
      "necessary conditions",
      "binomial collisions",
      "sufficiently large"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}