{
  "id": "1302.6061",
  "version": "v1",
  "published": "2013-02-25T11:43:09.000Z",
  "updated": "2013-02-25T11:43:09.000Z",
  "title": "Diophantine Approximation with Products of Two Primes",
  "authors": [
    "A. J. Irving"
  ],
  "comment": "25 pages",
  "doi": "10.1112/jlms/jdt079",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that for any irrational $\\alpha$ and any $\\tau<8/23$ there are infinitely many $n$ which are the product of two primes for which $$\\|n\\alpha\\|\\leq n^{-\\tau}.$$ We also show that for all sufficiently large $b$ there exist 3-digit palindromes in base $b$ with precisely two prime factors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-25T11:43:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "diophantine approximation",
      "prime factors",
      "irrational"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.6061I"
    }
  }
}