| 摘要: |
| 本文研究了指数Diophantine 方程4x + by =(b + 4)2 的解. 设b > 1 是给定的正奇数,运用有关指数Diophantine 方程的已知结果以及有关Pell 方程的Stormer 定理的推广, 证明了方程4x + by =(b + 4)2 仅有正整数解(x, y, z) =(1, 1, 1). |
| 关键词: 指数Diophantine方程 Pell方程 Stomer定理 |
| DOI： |
| 分类号:O156.7 |
| 基金项目:国家自然科学基金(11226038);陕西省自然科学基础研究计划资助项目(2014JM2-1010)资助. |
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| THE EXPONENTIAL DIOPHANTINE EQUATION 4x + by = (b + 4)2 |
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ZHU Min-hui1, LI Xiao-xue2
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1.School of Science, Xi'an Polytechnic University, Xi'an 710048, China;2.School of Mathematics, Northwest University, Xi'an 710127, China
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| Abstract: |
| In this paper, we study the solution of the exponential Diophantine equation 4x + by = (b + 4)2. Let b be a fixed odd positive integer with b > 1, using some known results on exponential Diophantine equations and an extension of the stormer theorem on Pell's equations, we prove that the equation 4x + by = (b + 4)2 has only the positive integer solution (x, y, z) = (1, 1, 1). |
| Key words: exponential Diophantine equation Pell's equations Stormer theorem |
