{
  "id": "0807.3010",
  "version": "v25",
  "published": "2008-07-18T16:54:30.000Z",
  "updated": "2008-11-21T02:40:47.000Z",
  "title": "Some conjectures on addition and multiplication of complex (real) numbers",
  "authors": [
    "Apoloniusz Tyszka"
  ],
  "comment": "11 pages, LaTeX2e, added various versions of Conjecture 5",
  "journal": "Int. Math. Forum 4 (2009), no. 9-12, pp. 521-530",
  "categories": [
    "math.CA"
  ],
  "abstract": "We discuss conjectures related to the following two conjectures: (1) for each complex numbers x_1,...,x_n there exist rationals y_1,...,y_n \\in [-2^{n-1},2^{n-1}] such that \\forall i \\in {1,...,n} (x_i=1 \\Rightarrow y_i=1) \\forall i,j,k \\in {1,...,n} (x_i+x_j=x_k \\Rightarrow y_i+y_j=y_k) (2) for each complex (real) numbers x_1,...,x_n there exist complex (real) numbers y_1,...,y_n such that \\forall i \\in {1,...,n} |y_i| \\leq 2^{2^{n-2}} \\forall i \\in {1,...,n} (x_i=1 \\Rightarrow y_i=1) \\forall i,j,k \\in {1,...,n} (x_i+x_j=x_k \\Rightarrow y_i+y_j=y_k) \\forall i,j,k \\in {1,...,n} (x_i \\cdot x_j=x_k \\Rightarrow y_i \\cdot y_j=y_k)",
  "revisions": [
    {
      "version": "v25",
      "updated": "2008-11-21T02:40:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B30",
      "12D99",
      "14P05",
      "15A06",
      "15A09"
    ],
    "keywords": [
      "conjectures",
      "multiplication"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.3010T"
    }
  }
}