| 一类Pythagoras问题的推广 |
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| 引用本文： | 管训贵. 一类Pythagoras问题的推广[J]. 唐山学院学报, 2012, 25(3): 7-9 |
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| 作者姓名： | 管训贵 |
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| 作者单位： | 泰州师范高等专科学校数理信息学院,江苏泰州,225300 |
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| 摘 要： | 设x,y,z是正整数.若x2+y2=z2,则称(x,y,z)是一组Pythagoras数.本文运用初等方法证明了:(1)恰有12组Pythagoras数(x,y,z)满足2p(x,y,z)=xy,其中p为奇素数;(2)恰有36组Pythagoras数(x,y,z)满足2pq(x+y+z)=xy,其中p,q均为奇素数,且p
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| 关 键 词： | Pythagoras数 奇素数 约束条件 计数 |
Generalization of a Class of Pythagoras Problems |
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| GUAN Xun-gui. Generalization of a Class of Pythagoras Problems[J]. Journal of Tangshan College, 2012, 25(3): 7-9 |
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| Authors: | GUAN Xun-gui |
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| Affiliation: | GUAN Xun-gui(School of Mathematics,Physics and Information Science,Taizhou Normal College,Taizhou 225300,China) |
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| Abstract: | Let x,y,z be positive integers.If x2+y2=z2,then(x,y,z) is called a Pythagoras triplet.In this paper,using some elementary methods,we prove that(1) exist exactly 12 Pythagoras triplets(x,y,z) satisfying 2p(x+y+z)=xy,where p be an odd prime;(2)exist exactly 36 Pythagoras triplets(x,y,z) satisfying 2pq(x+y+z)=xy,where p,q are odd primes with p
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| Keywords: | Pythagoras triplets odd prime restricted condition enumeration |
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