{
  "id": "2501.17136",
  "version": "v2",
  "published": "2025-01-28T18:34:55.000Z",
  "updated": "2025-02-04T18:27:54.000Z",
  "title": "On Monochromatic Solutions of Linear Equations Using At Least Three Colors",
  "authors": [
    "Laurence P. Wijaya"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We study the number of monochromatic solution to linear equation in $\\{1,\\dots,n\\}$ when we color the set by at least three colors. We consider the $r$-commonness for $r\\geq 3$ of linear equation with odd number of terms, and we also prove that any $2$-uncommon equation is $r$-uncommon for any $r\\geq 3$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2025-02-04T18:27:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05D10",
      "05E16",
      "11B75"
    ],
    "keywords": [
      "linear equation",
      "monochromatic solution",
      "odd number",
      "uncommon equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}