{
  "id": "0911.5665",
  "version": "v59",
  "published": "2009-11-30T19:57:02.000Z",
  "updated": "2011-10-05T19:57:43.000Z",
  "title": "Open Conjectures on Congruences",
  "authors": [
    "Zhi-Wei Sun"
  ],
  "comment": "88 pages. For new additions, see Conj. A76-85",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while conjectures in Part B have been recently confirmed. We hope that this material will interest number theorists and stimulate further research. Number theorists are welcome to work on those open conjectures; for some of them we offer prizes for the first correct proofs.",
  "revisions": [
    {
      "version": "v59",
      "updated": "2011-10-05T19:57:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "11A07",
      "11A41",
      "11B68",
      "05A10",
      "05A15",
      "11E25",
      "11S99",
      "33C20",
      "65B10"
    ],
    "keywords": [
      "open conjectures",
      "congruences",
      "binary quadratic forms",
      "interest number theorists",
      "first correct proofs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 88,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.5665S"
    }
  }
}