Work

Rational points in geometric progression on the unit circle

Year: 2021

Type: article

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 $3$.

Source: Publicationes Mathematicae Debrecen

DOI: 10.5486/pmd.2021.9046

Authors: Gamze Savas Celik, Mohammad Sadek, Gokhan Soydan

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Bursa Uludağ Üniversitesi

OpenAlex ID: W3091900673

FWCI:

Cites: 23

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Related to: 20