{
  "id": "2010.03830",
  "version": "v1",
  "published": "2020-10-08T08:14:40.000Z",
  "updated": "2020-10-08T08:14:40.000Z",
  "title": "Rational Points in Geometric Progression on the Unit Circle",
  "authors": [
    "Gamze Savaş Çelik",
    "Mohammad Sadek",
    "Gökhan Soydan"
  ],
  "comment": "7 pages, accepted for publication in Publicationes Mathematicae Debrecen",
  "categories": [
    "math.NT"
  ],
  "abstract": "A sequence of rational points on an algebraic planar curve is said to form an $r$-geometric progression sequence if either the abscissae or the ordinates of these points form a geometric progression sequence with ratio $r$. In this work, we prove the existence of infinitely many rational numbers $r$ such that for each $r$ there exist infinitely many $r$-geometric progression sequences on the unit circle $x^2 + y^2 = 1$ of length at least $3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-08T08:14:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "14G05"
    ],
    "keywords": [
      "unit circle",
      "rational points",
      "geometric progression sequence",
      "algebraic planar curve",
      "points form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}