Rational points in geometric progression on the unit circle

Official URL: https://dx.doi.org/10.5486/PMD.2021.9046

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 x2 + y2 = 1 of length at least 3.