| 关于指数丢番图方程a2x+(3a2-1)y=(4a2-1)z |
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| 引用本文： | 胡永忠. 关于指数丢番图方程a2x+(3a2-1)y=(4a2-1)z[J]. 数学进展, 2007, 36(4): 429-434 |
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| 作者姓名： | 胡永忠 |
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| 作者单位： | 中南大学数学科学与计算技术学院,长沙,湖南,410075;佛山科学技术学院数学系,佛山,广东,528000 |
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| 摘 要： | 设a＞3是一个整数,应用Bilu,Hanrot和Voutier关于本原素除子的深刻理论以及二次数域类数的一些结果,证明了指数丢番图方程a2x＋（3a2-1）y=（4a2-1）z仅有正整数解x=y=1.
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| 关 键 词： | 指数丢番图方程 Lucas序列 本原素除子 Kronecker(Legendre)符号 |
| 文章编号： | 1000-0917（2007）04-0429-06 |
| 修稿时间： | 2005-06-16 |
On the Exponential Diophantine Equation a2x+(3a2-1)y=(4a2-1)z |
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| HU Yongzhong. On the Exponential Diophantine Equation a2x+(3a2-1)y=(4a2-1)z[J]. Advances in Mathematics(China), 2007, 36(4): 429-434 |
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| Authors: | HU Yongzhong |
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| Affiliation: | School of Mathematical Sciences and Computing Technology Central South University, Changsha, Hunan, 410075, P. R. China;Department of Mathematics, Foshan University, Foshan, Guangdong, 528000, P.R. China;Department of Mathematics, Foshan University, Fosha |
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| Abstract: | Let a ＞ 3 be an integer, we apply a new, deep theorem of Bilu, Hanrot & Voutier and some results on the class number of quadratic field to show that the only positive integer solution of the exponential Diophantine equation a2x+(3a2-1)y=(4a2-1)z is x = y = z = 1. |
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| Keywords: | exponential Diophantine equations Lucas sequences primitive divisors Kronecker(Legendre) symbol |
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