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3维勾股数的性质及其计算方法 被引量:3

The Properties of Three-dimensional Pythagorean Triple and its Calculation Method
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摘要 讨论了3维本原勾股数的几条性质,并根据2维勾股数与3维勾股数的关系,提出了用2维本原勾股数构造3维勾股数的方法和计算公式。从三元数的概念出发,推导出计算3维本原勾股数的公式及其计算结果。利用该方法可以类推出4维、5维甚至更高维勾股数。 In this paper,some properties of the 3D primitive pythagorean triangles were discussed,and on the basis of the relation between the two dimension pythagorean triangles and the 3D pythagorean triangles,a method and a design formula of constructing the 3D pythagorean triangles by utilizing two dimension Primitive pythagorean triangles.A design formula of the 3D primitive pythagorean triangles which is according to the three-ary number was inferred and applied as well.This design formulas can be used to infer the design formulas of four-dimensional pythagorean triangles,five-dimensional pythagorean triangles,and even more dimensional pythagorean triangles
作者 颜有祥
出处 《新乡学院学报》 2010年第3期3-6,共4页 Journal of Xinxiang University
关键词 不定方程 正整数解 3维本原勾股数 导出勾股数 三元数 diophantine equation positive integer solution the 3D primitive pythagorean triple derivative pythagorean triple the three-ary number
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同被引文献4

  • 1[美]Joseph H Silverman.数论概论[M].孙志伟,等泽.北京:机械工业出版社,2008:24-25.
  • 2闽嗣鹤,严士键.初等数论(第三版)[M].北京:高等教育出版社,2003.
  • 3闽嗣鹤,严士键.初等数论[M].3版.北京:高等教育出版社,2003:109-114.
  • 4SILVERMANJH.数论概论[M].孙智伟,吴克检,卢青林,等译.北京:机械工业出版社,2008:54-129.

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