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

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

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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)

Abstract

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

[ 1] MAHLER K. Zur Approximation Algebraischer Zahlen I: ??berden Qr??ssfen Primtailer Bin??rer Formen [ J] . Math. Ann. , 1933, ( 107) :691- 730.

[ 2] GEL??FOND A O. Sur la Divisibilit?? de la Diff??rence Des Puissances de Deux Nombres Entiers Par Une Puissance d??un id??al Premier[ J] . Mat. Sb. , 1940, ( 7) : 7- 25.

[ 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.

[ 11] TERAI N.The Diophantine Equation ax + by = cz ?? [ J] . Proc. Japan Acad Ser. A. Math. Sci. , 1995, 71: 109- 110.

[ 12] TERAI N.The Diophantine Equation ax + by = cz ?? [ J] . Proc. Japan Acad Ser. A. Math. Sci. , 1996, 72: 20- 22.

[ 13] TERAI N, TAKAKUWA K. A Note on the Diophantine Equation ax + by = cz [ J] . Proc. Japan Acad. Ser . A. Math. Sci. , 1997,73: 161- 164.

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

[1]	DENG Mou-Jie, ZHOU Xiao-E. Computer Aided Solution of the Diophantine Equation 5·2^x+7·3^y=11+2^z·3^w [J]. journal6, 2013, 34(6): 1-3.
[2]	LE Mao-Hua. On the Ternary Exponential Diophantine Equation for Generalized Pythagorean Triplets [J]. journal6, 2011, 32(5): 1-8.
[3]	LE Mao-Hua. Upper Bounds for Solutions of the Lebesgue-Nagell Equation [J]. journal6, 2011, 32(3): 4-7.
[4]	SONG Rong-Yan, DENG Mou-Jie. On the Diophantine Equation 1+7^x=2^y5^z+2^u5^v7^w [J]. journal6, 2011, 32(1): 4-6.
[5]	LE Mao-Hua. On the Exponential Diophantine Equation n^x+(n+2)^y=(n+1)^z [J]. journal6, 2010, 31(4): 5-7.
[6]	DENG Mou-Jie, LI Chun-Yan. On the Diophantine Equation 1+2^x7^y+2^z5^u7^v=5^w [J]. journal6, 2009, 30(4): 1-3.
[7]	HUANG Yong-Qing. On the Diophantine Equation x³－8＝61y² [J]. journal6, 2006, 27(6): 24-25.
[8]	LE Mao-Hua. On the Diophantine Equation x³+3^3m=2Dy² [J]. journal6, 2005, 26(1): 1-2.
[9]	LE Mao-Hua. Perfect Powers in Fermat Quotients [J]. journal6, 2003, 24(3): 1-2.
[10]	LE Mao-Hua. The Number of Solutions of Simultaneous Pell Equations [J]. journal6, 2003, 24(2): 1-9.
[11]	LE Mao-Hua. A Conjecture Concerning an Exponential Diophantine Equation [J]. journal6, 2003, 24(1): 1-4.
[12]	LE Mao-Hua. On the Number of Solutions of the Generalized Ramanujan-Nagell Equation x²+D=4pⁿ [J]. journal6, 2002, 23(3): 44-46.
[13]	LE Mao-Hua. The Diophantine Equation 2^m+1=3yⁿ [J]. journal6, 2001, 22(2): 1-4.
[14]	LE Mao-Hua. The Number of Solutions for a Class of Exponential Diophantine Equations [J]. journal6, 2000, 21(3): 27-32.

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

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