{
  "id": "1205.0371",
  "version": "v1",
  "published": "2012-05-02T10:37:29.000Z",
  "updated": "2012-05-02T10:37:29.000Z",
  "title": "Mersenne Primes in Real Quadratic Fields",
  "authors": [
    "Sushma Palimar",
    "Shankar B. R"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "The concept of Mersenne primes is studied in real quadratic fields of class number 1. Computational results are given. The field $Q(\\sqrt{2})$ is studied in detail with a focus on representing Mersenne primes in the form $x^{2}+7y^{2}$. It is also proved that $x$ is divisible by 8 and $y\\equiv \\pm3\\pmod{8}$ generalizing the result of F Lemmermeyer, first proved in \\cite{LS} using Artin's Reciprocity law.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-02T10:37:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R11",
      "11Y11"
    ],
    "keywords": [
      "real quadratic fields",
      "artins reciprocity law",
      "class number",
      "computational results",
      "representing mersenne primes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.0371P"
    }
  }
}