Rational Points in Geometric Progression on the Unit Circle
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 x2 + y2 = 1 of length at least 3.
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