| Evans问题的一类新解 |
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| 引用本文： | 边欣,李忠民.Evans问题的一类新解[J].北京联合大学学报(自然科学版),2011(2):68-69. |
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| 作者姓名： | 边欣 李忠民 |
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| 作者单位： | 1. 天津师范大学,数学系,天津,300387
2. 天津大学,管理与经济学部,天津,300072 |
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| 摘 要： | 利用问题E2687解的一个充要条件,构造出一类新的本原Evans三角形,其三边长分别为k2-2+4k2(k2-2)(k2-1)3,1+4k2(k2-2)(k2-1)3,k2-1;且三角形中最短边上的高与该边长之比是4k(k2-2)(2k4-4k2+1)型的整数,其中k>1是正整数。
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| 关 键 词： | 问题E2687 整数边三角形 Evans三角形 Evans比 |
A New Solution to Evans Problem |
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| BIAN Xin,LI Zhong-min.A New Solution to Evans Problem[J].Journal of Beijing Union University,2011(2):68-69. |
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| Authors: | BIAN Xin LI Zhong-min |
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| Institution: | BIAN Xin1,LI Zhong-min2(1.Department of Mathematics,Tianjin Normal University,Tianjin 300387,China,2.Department of Management and Economics,Tianjin University,Tianjin 300072,China) |
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| Abstract: | By a necessary and sufficient condition of Problem E2687,a new family of Primitive Evans triangles is established.The three sides of the triangles are respectively k2-2+4k2(k2-2)(k2-1)3,1+4k2(k2-2)(k2-1)3 and k2-1,and the ratio of the height on the shortest side of the triangles to the length of the same side is an integer of 4k(k2-2)(2k4-4k2+1),with k>1 being a positive integer. |
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| Keywords: | problem E2687 integer-sided triangles Evans triangles Evans ratios |
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