A Jacobi Symbol Concerning the Exponential Diophantine Equation ax+by=cz
( 1. Department of Mathematics, Zhanjiang Normal College, Zhanjiang 524037, Guangdong China;2. Department of Mathematics, Shanghai Teachers s University, Shanghai 200234, China)
Online:2004-03-15
Published:2012-11-06
About author:LE Mao-hua( 1952- ) , male, was born in Shanghai, the professor of the department of Mathematics, Zhanjiang Normal Collage, research area is number theory.
Supported by:
Supported by the National Natural Science Foundation of China ( No. 10271104) , the Guangdong Provincial Natural Science Foundation( No. 011781) and the Natural Science Foundation of Education Department of Guangdong Province ( No.0161)
摘要：设r 是大于1 的奇数, u, v 是适合2 | u, gcd( u , v ) = 1, u > 2r v/ ?? 的正整数. 又设a, b , c 是适合a+ b - 1 = ( u+ v - 1) r 以及c = u2 + v 2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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