| 关于指数Diophantine方程ax+by=cz的一个猜想 |
| |
| 引用本文： | 乐茂华.关于指数Diophantine方程ax+by=cz的一个猜想[J].黑龙江大学自然科学学报,2003,20(2):10-14. |
| |
| 作者姓名： | 乐茂华 |
| |
| 作者单位： | 湛江师范学院,数学系,广东,湛江,524048 |
| |
| 基金项目： | Supported by the National Natural Science Foundation of China(10271104)，the Guangdong Provincial Natural Science Foundation(011781)，the Natural Science Foundation of Education Department of Guangdong Province(0161) |
| |
| 摘 要： | 设r是大于1的正奇数,m是偶数.设Ur,Vr是适合Vr+Ur√-1=(m+√-1)r的整数,又设a=|Vr|,b=|Ur|,c=m2+1.证明了当a≡2(mod
4),b≡3(mod 4),m≥41r3/2时,方程ax+by=cz仅有正整数解(x,y,z)=(2,2,r).
|
| 关 键 词： | 指数Diophantine方程 正整数解 Terai猜想 |
A conjecture concerning the exponential Diophantine equation ax +by=cz |
| |
| Abstract.A conjecture concerning the exponential Diophantine equation ax +by=cz[J].Journal of Natural Science of Heilongjiang University,2003,20(2):10-14. |
| |
| Authors: | Abstract |
| |
| Abstract: | Let r be an odd integer with r>1, and let m be an even integer. Let a=|Vr|,b=|Ur|, c=m2+1, where Ur, Vr are integers satisfying V,+ Ur-1 = (m+-1)r. It will be prowed that if a=2(mod 4), b=3(mod 4) and m>41r3/2, then the equation ax+by=cz has only the positive integer solution (x,y,z)=(2, 2, r). |
| |
| Keywords: | Exponential Diophantine equation positive integer solution Terai conjecture |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
