{
  "id": "math/0703467",
  "version": "v1",
  "published": "2007-03-15T19:10:18.000Z",
  "updated": "2007-03-15T19:10:18.000Z",
  "title": "On sequences of positive integers having no $p$ terms in arithmetic progression",
  "authors": [
    "Goutam Pal"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We use topological ideas to show that, assuming the conjecture of Erd\\\"(o)s on subsets of positive integers having no $p$ terms in arithmetic progression (A. P.), there must exist a subset $M_p$ of positive integers with no $p$ terms in A. P. with the property that among all such subsets, $M_p$ maximizes the sum of the reciprocals of its elements.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-15T19:10:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive integers",
      "arithmetic progression",
      "conjecture",
      "reciprocals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3467P"
    }
  }
}