{
  "id": "1401.2869",
  "version": "v1",
  "published": "2014-01-13T15:18:34.000Z",
  "updated": "2014-01-13T15:18:34.000Z",
  "title": "A basis of the group of primitive almost pythagorean triples",
  "authors": [
    "Nikolai A. Krylov"
  ],
  "comment": "10 pages, continuation of arXiv:1107.2860",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $m$ be a fixed square-free positive integer, then equivalence classes of solutions of Diophantine equation $x^2+m\\cdot y^2=z^2$ form an infinitely generated abelian group under the operation induced by the complex multiplication. A basis of this group is constructed here using prime ideals and the ideal class group of the field $\\mathbb Q (\\sqrt{-m})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-13T15:18:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11R11",
      "20F05"
    ],
    "keywords": [
      "pythagorean triples",
      "ideal class group",
      "equivalence classes",
      "diophantine equation",
      "infinitely generated abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}