| 广义Ramanujan-Nagell方程x~2-D=3~n的解数 |
| |
| 引用本文： | 杨继明.广义Ramanujan-Nagell方程x~2-D=3~n的解数[J].数学学报,2008,51(2):351-356. |
| |
| 作者姓名： | 杨继明 |
| |
| 作者单位： | 玉溪师范学院数学系,玉溪653100 |
| |
| 摘 要： | 设D是不能被3整除的正整数.本文证明了:当D>1012时,如果Pell方程U2-DV2=-1有解(U,V),则方程x2-D=3n至多有2组正整数解(x,n).
|
| 关 键 词： | 指数Diophantine方程 解数 上界 |
| 文章编号： | 0583-1431（2008）02-0351-06 |
| 收稿时间： | 2006-03-14 |
The Number of Solutions of the Generalized Ramanujan-Nagell Equation x~2-D=3n |
| |
| Ji Miag YANG.The Number of Solutions of the Generalized Ramanujan-Nagell Equation x~2-D=3n[J].Acta Mathematica Sinica,2008,51(2):351-356. |
| |
| Authors: | Ji Miag YANG |
| |
| Institution: | Ji Ming YANG Department of Mathematics, Yuxi Normal University, Yuxi 653100, P. R. Chian |
| |
| Abstract: | Let D be a positive integer with D■0 (mod 3). In this paper we prove that if D > 1012 and the Pell equation U2 - DV2 = -1 has solutions (U, V), then the equation x2 - D = 3n has at most two positive integer solutions (x, n). |
| |
| Keywords: | exponential Diophantine equation number of solutions upper bound |
| 本文献已被 维普 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
| 点击此处可从《数学学报》下载免费的PDF全文 |
|
