Rational points in geometric progression on the unit circle

Celik G. S., Sadek M., SOYDAN G.

PUBLICATIONES MATHEMATICAE-DEBRECEN, vol.98, pp.513-520, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 98
  • Publication Date: 2021
  • Doi Number: 10.5486/pmd.2021.9046
  • Journal Name: PUBLICATIONES MATHEMATICAE-DEBRECEN
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.513-520
  • Bursa Uludag University Affiliated: Yes

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.