{
  "id": "1710.06023",
  "version": "v1",
  "published": "2017-10-16T22:56:10.000Z",
  "updated": "2017-10-16T22:56:10.000Z",
  "title": "Almost Universal Weighted Ternary Sums of Polygonal Numbers",
  "authors": [
    "Siu Hang Man",
    "Archie Mehta"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "For a natural number $m$, generalized $m$-gonal numbers are defined by the formula $p_m(x)=\\frac{(m-2)x^2-(m-4)x}{2}$ with $x\\in \\mathbb Z$. In this paper, we determine a criterion on $a,b,c,m$ for which the weighted ternary sum $P_{a,b,c,m}:=ap_m(x)+bp_m(y)+cp_m(z)$ is almost universal. We also prove for some $a,b,c,m$ that the form $P_{a,b,c,m}$ is not almost universal, while it represents all possible congruence classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-16T22:56:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11E20",
      "11E25",
      "11E45",
      "11E81",
      "11H55",
      "05A30"
    ],
    "keywords": [
      "universal weighted ternary sums",
      "polygonal numbers",
      "natural number",
      "congruence classes",
      "represents"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}