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| 摘要: |
| 设D > 1是正整数，p是适合p|D的素数.本文研究了指数Diophantine方程x2=D2m-Dmpn+p2n的满足m > 1的正整数解.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满足m > 1的所有正整数解（D，p，x，m，n）.这个结果修正并完整解决了文献[4]的猜想. |
| 关键词: 指数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）. |
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| ON THE EXPONENTIAL DIOPHANTINE EQUATION x2=D2m -Dmpn + p2n |
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HE Yan-feng
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| Abstract: |
| Let D be a positive integer with D > 1, and p be a prime with p|D. In this paper, we study the positive integer solutions of the Diophantine equation x2=D2m-Dmpn + p2n with m > 1. By using properties and several known results of Diophantine equations with some elementary methods, all positive integer solutions (D, P, x, m, n) of the equations x2=D2m-Dmpn + p2n are determined, which corrects and completely solves the presumption in[4]. |
| Key words: exponential Diophantine equation positive integer solution elementary method |
