论文标题
单位圆几何进程的理性点
Rational Points in Geometric Progression on the Unit Circle
论文作者
论文摘要
如果脱节或这些点的求和序列形成比率$ r $的几何进程序列，则认为代数平面曲线上的一系列理性点被认为会形成$ r $ $的几何进程序列。在这项工作中，我们证明存在无限的许多理性数字$ r $，因此对于每个$ r $，在单位圆圈$ x^2 + y^2 = 1 $长度至少$ 3 $上都存在无限的许多$ r $ r $ - 几何进程序列。
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 $3$.
