| 关于方程multiply from i=1 to k(x_i~(x_i))=Z~Z的奇数解 |
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| 引用本文： | 姚兆栋.关于方程multiply from i=1 to k(x_i~(x_i))=Z~Z的奇数解[J].湖北大学学报(自然科学版),1988(3). |
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| 作者姓名： | 姚兆栋 |
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| 作者单位： | 湖北大学空军雷达学院 |
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| 摘 要： | 柯召、孙琦在2]中研究了方程multiply from i=1 to k (x_i~xi)=Z~z 当(x_1,x2,……x_k,z)>1时,对任意的k,方程(2)都有无穷多个整数解(偶数解)、对特殊的某些k,证明了方程(2)有奇数解。本文将证明当k>3,(k=4,5,……)的所有k,方程(2)都有奇数解,同时本文的定理3将给出方程(2)的新整数解(偶数解),不难看出,它包含了2],3]中得到的偶数解。
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| 关 键 词： | 整数解 奇(偶)数解 |
ON THE ODD INTEGRAL SOLUTIONS OF THE EGUATION multiply from i=1 to k(x_i~(x_i))=Z~Z |
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| Yao Zhaodong.ON THE ODD INTEGRAL SOLUTIONS OF THE EGUATION multiply from i=1 to k(x_i~(x_i))=Z~Z[J].Journal of Hubei University(Natural Science Edition),1988(3). |
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| Authors: | Yao Zhaodong |
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| Institution: | The Institute of Air Force Radar |
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| Abstract: | Ke Zhao and Sun Qi studied the equation
when k>3 and(x1,i,..., xk, Z)>1,They proved that the given equation has infinitely many even integral solutions for any integer k>3 and has odd integral solutions for some special integers KIn this paper,We shall prove that the given equation has odd integral solutions for all k>3 At the same time our theorem 3 will give a set of new even integral solutions which involves the even integral solutions given in 2]and3] |
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| Keywords: | Integral solutisn odd (even) integral solution |
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