| 摘要: |
| 设a=|m4-6m2+1|,b=4m3-4m,c=m2+1,且2|m,利用Jacobi符号以及广义Fermat方程的已有解,证明指数丢番图方程ax+by=cz仅有正整数解(x,y,z)=(2,2,4). |
| 关键词: 指数丢番图方程 解 Jacobi符号 Terai猜想 |
| DOI： |
| 投稿时间：2006-06-12 |
| 基金项目:四川省教育厅自然科学(2006C057)基金和阿坝师专校级科研基金项目(ASB06-07)资助。 |
|
| On the Solutions of the Exponential Diophantine Equation|m4-6m2+1|x+ (4m3-4m)y=(m2+l)z |
|
YANG Shi-chun
|
| (A'Ba Teachers College, Wenchuan, Sichuan, 623000, China) |
| Abstract: |
| Let a=|m4-6m2+l|,b=4m3-4m,c=m2+1, where 2|m,m∈N. In terms of Jacobi symbol, and a deep result of generalized Fermat equation, it is proved that the diophantine equation ax+by=cz has only one positive integer solution (x,y,z)=(2,2,4). |
| Key words: exponential diophantine equation solutions Jacobi symbol Terai's conjecture |
