| 关于指数丢番图程ax+by=cz的一个Jacobi符号 |
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| 引用本文： | 乐茂华. 关于指数丢番图程ax+by=cz的一个Jacobi符号[J]. 吉首大学学报(自然科学版), 2004, 25(1): 1-2 |
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| 作者姓名： | 乐茂华 |
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| 作者单位： | 湛江师范学院数学系,广东,湛江,524037;上海师范大学数学系,上海,200234 |
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| 基金项目： | SupportedbytheNationalNaturalScienceFoundationofChina (No .10 2 7110 4 )，theGuangdongProvincialNatu ralScienceFoundation(No.011781)andtheNaturalScienceFoundationofEducationDepartmentofGuangdongProvince (No.0 16 1) |
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| 摘 要： | 设r是大于 1的奇数 ,u ,v是适合 2 ｜u ,gcd(u ,v) =1,u >2rv/π的正整数 .又设a ,b ,c是适合a+b - 1=(u+v - 1) r 以及c=u2 +v2 的正整数 .确定了Jacobi符号的值 .这一结果有助于指数Diophantine方程ax+by =cz 的求解
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| 关 键 词： | 指数Diophantine方程 解数 Jacobi符号 |
A Jacobi Symbol Concerning the Exponential Diophantine Equation ax+by=cz |
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| Abstract. A Jacobi Symbol Concerning the Exponential Diophantine Equation ax+by=cz[J]. Journal of Jishou University(Natural Science Edition), 2004, 25(1): 1-2 |
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| Authors: | Abstract |
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| Affiliation: | ( 1. Department of Mathematics, Zhanjiang Normal College, Zhanjiang 524037, Guangdong China;2. Department of Mathematics, Shanghai Teachers s University, Shanghai 200234, China) |
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| Abstract: | Let r be and odd integer with r>1,and let u,v be positive integers such that 2|u gcd (u,v)and u 2rv>/π,Further let a,b,c be positive integers satisfying a+b(-1)=(u+v(-1))r and c=u2+v2.The value of Jacobi symbol(b/v)/(a/u) is determined. This result can be used for solving the exponential diophanitine equation ax+bx=c2 |
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| Keywords: | Exponential diophantine equation number of solutions Jacobi symbol |
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