| 摘要: |
| 设\;$D>1$\;是正整数, $p$\;是适合\;$p\nmid D$\;的素数. 本文根据\;$Diophantine$\;方程的性质, 结合已有的结论, 运用初等方法确定了方程: $x^2=D^{2m}-D^mp^n+p^{2n}$\;的所有适合\;$m>1$\;的所有正整数解:\;$(D, p, x, m, n)$ |
| 关键词: Diophantine 方程 正整数解 初等方法 |
| DOI： |
| 分类号:O156.7 |
| 基金项目:陕西省科技厅项目(2013JQ1019), 延安大学自然科学基金项目(YDK201101) |
|
| ON THE EXPONENTIAL DIOPHANTINE EQUATION $x^2=D^{2m}-D^mp^n+p^{2n}$ |
|
He Yanfeng
|
|
College of Mathematics and Computer Science, Yan'an University, Yan'an,Shaanxi
|
| Abstract: |
| Let $D$ be a positive integer with $D>1$, and let $p$ be a prime with $p\nmid D$. In this paper, by using properties and certain known results of diophantine equations with some elementary metholds, all positive integer solutions $(x,m,n)$ of the
equations $x^2=D^{2m}-D^mp^n+p^{2n}$ are determined. |
| Key words: exponential diophantine equation positive integer solution elementary method |
