关于指数丢番图程ax+by=cz的一个Jacobi 符号

journal6 ›› 2004, Vol. 25 ›› Issue (1): 1-2.

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关于指数丢番图程a^x+b^y=c^z的一个Jacobi 符号

( 1. 湛江师范学院数学系, 广东湛江524037; 2. 上海师范大学数学系, 上海200234)

出版日期:2004-03-15 发布日期:2012-11-06

A Jacobi Symbol Concerning the Exponential Diophantine Equation a^x+b^y=c^z

( 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/Abstract

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a^x+b^y=c^z的求解.

关键词： 指数Diophantine 方程, 解数, Jacobi 符号

Abstract: Let r be an odd integer with r > 1 , and let u, v be positive integers such that 2 | u gcd ( u, v ) and u > 2r v????, 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 diophantine equation a^x+b^y=c^z

Key words: Exponential diophantine equation, number of solutions, Jacobi symbol

乐茂华. 关于指数丢番图程a^x+b^y=c^z的一个Jacobi 符号[J]. journal6, 2004, 25(1): 1-2.

LE Mao-Hua. A Jacobi Symbol Concerning the Exponential Diophantine Equation a^x+b^y=c^z[J]. journal6, 2004, 25(1): 1-2.

参考文献

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[ 3] TERAI N.The Diophantine Equation ax + by = cz [ J] . Proc. Japan Acad. Ser. A Math. Sci. , 1994, 70: 22- 26.

[ 4] CAO Z- F. A Note on the Diophantine Equation ax + by = cz [ J] . Acta Arith, 1999, 91: 85- 93.

[ 5] LEMao- hua. On the Diophantine Equation ax + by = cz [ J] . Journal of Changchun Teachers College( Naturnal Sciences Edition) ,1985, 2( 1) : 50- 62.

[ 6] LE Mao- hua. A Note on the Diophantine Equation ( m3 - 3m) x + ( 3m2 - 1) y = ( m2 + 1) z [ J] . Proc. Japan Acad Ser . A Math.Sci. , 1997, 73: 148- 149.

[ 7] LE Mao- hua. On Terai??s Conjecture Concerning Pythagorean Numbers [ J] . Bull. Austral Math. Soc. , 2000, 61: 329- 334.

[ 8] LE Mao- hua. On the Exponential Diophantine Equation ( m3 - 3m) x + ( 3m2- 1) y = ( m2 + 1) z [ J] . Publ. Math. Debrecen, 2001,58: 461- 466.
[ 9] LE Mao- hua. A Conjecture Concerning the Exponential Diophantine Equation ax + by = cz [ J] . Acta. Arith, 2003, 106: 345- 353.

[ 10] LE Mao- hua. On the Terai??s Conjecture Concerning the Exponential Diophantine Equation ax + by = cz [ J] . Acta Mathematica Sin-ica, 2003, 46( 2) : 245- 250.

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[ 14] LE Mao-hua. An Open Problem Concerning the Exponential Diophantine Equation ax + by = cz [ J] . Publ. Math. Debrecen, to appear.

[1]	乐茂华. 联立Pell方程组的解数[J]. journal6, 2003, 24(2): 1-9.
[2]	乐茂华. 关于指数Diophantine方程的1个猜想[J]. journal6, 2003, 24(1): 1-4.
[3]	乐茂华. 关于广义Ramanujan-Nagell方程x²+D=4pⁿ的解数[J]. journal6, 2002, 23(3): 44-46.
[4]	乐茂华. 一类指数丢番图方程的解数[J]. journal6, 2000, 21(3): 27-32.

关于指数丢番图程a^x+b^y=c^z的一个Jacobi 符号

A Jacobi Symbol Concerning the Exponential Diophantine Equation a^x+b^y=c^z

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关于指数丢番图程ax+by=cz的一个Jacobi 符号

A Jacobi Symbol Concerning the Exponential Diophantine Equation ax+by=cz

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关于指数丢番图程a^x+b^y=c^z的一个Jacobi 符号

A Jacobi Symbol Concerning the Exponential Diophantine Equation a^x+b^y=c^z