具有公共面积和公共周长的积分三角形和垂直四边形对

IF 0.5 Q3 MATHEMATICS
A. S. Zargar, Yong Zhang
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引用次数: 1

摘要

利用椭圆曲线理论,我们证明了有无限多个面积和周长相同的积分直角三角形-垂直四边形、积分等腰三角形-垂直边形和Heron三角形-垂直四边形对。此外,对于与积分等腰三角形和积分垂直四边形对相关的椭圆曲线,我们给出了秩为$\geq4$的几个亚族,并证明了秩为$\geq5$的无限多条椭圆曲线的存在性,这些椭圆曲线由正秩椭圆曲线的点参数化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Integral triangles and perpendicular quadrilateral pairs with a common area and a common perimeter
By the theory of elliptic curves, we show that there are infinitely many integral right triangle-perpendicular quadrilateral, integral isosceles triangle-perpendicular quadrilateral, and Heron triangle-perpendicular quadrilateral pairs with a common area and a common perimeter. Moreover, for the elliptic curve associated to integral isosceles triangle and integral perpendicular quadrilateral pairs, we present several subfamilies of rank $\geq 4$, and show the existence of infinitely many elliptic curves of rank $\geq 5$, parameterized by the points of an elliptic curve of positive rank.
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来源期刊
CiteScore
0.80
自引率
20.00%
发文量
14
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