Publication:
Rational points in geometric progression on the unit circle

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Date

2021-01-01

Authors

Çelik, Gamze Savaş

Authors

Çelik, Gamze Savaş
Sadek, Mohammad
Soydan, Gökhan

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Kossuth Lajos Tudomanyegyetem

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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.

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Keywords

Elliptic curve, Geometric progression, Huff curve, Rational point, Unit circle, Science & technology, Physical sciences, Mathematics

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