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引用次数: 0
摘要
本文研究圆锥曲线上的长算术级数。所谓曲线上的算术级数，是指曲线上存在 x 坐标在算术级数中的有理点。我们重温了单位圆上的算术级数，构建了包含单位圆上任意有理点的第一象限中点的三项级数。我们还提供了单位双曲线上三项级数的无穷族，以及包含长达 8 项级数的算术级数的圆锥 ax2 + cy2 = 1。
In this paper, we look at long arithmetic progressions on conics. By an arithmetic progression on a curve, we mean the existence of rational points on the curve whose x-coordinates are in arithmetic progression. We revisit arithmetic progressions on the unit circle, constructing 3-term progressions of points in the first quadrant containing an arbitrary rational point on the unit circle. We also provide infinite families of three term progressions on the unit hyperbola, as well as conics ax2 + cy2 = 1 containing arithmetic progressions as long as 8 terms.
期刊介绍：
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