| 几个不定方程在mathbf{Q}(sqrt{-3})中的解（英） |
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| 引用本文： | 王永亮. 几个不定方程在mathbf{Q}(sqrt{-3})中的解（英）[J]. 华东师范大学学报(自然科学版), 2009, 2009(5): 138-141 |
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| 作者姓名： | 王永亮 |
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| 作者单位： | 菏泽学院数学系,菏泽,274015 |
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| 摘 要： | 应用Fermat下降法，证明了不定方程~{x^{4}-y^{4}=z^{2}} 与~{x^{4}+4y^{4}=z^{2}} 在 {mathbf{Q}}(sqrt{-3}) 没有非平凡解, 它表明Fermat方程当~n=4时在此域中仍然没有非平凡解.
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| 关 键 词： | Fermat下降法 代数整数环 虚二次域 Fermat下降法 代数整数环 虚二次域 |
| 收稿时间： | 2008-09-24 |
| 修稿时间： | 2009-02-10 |
Solutions to some Diophantine equations over mathbf{Q}(sqrt{-3} |
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| WANG Yong-liang. Solutions to some Diophantine equations over mathbf{Q}(sqrt{-3}[J]. Journal of East China Normal University(Natural Science), 2009, 2009(5): 138-141 |
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| Authors: | WANG Yong-liang |
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| Affiliation: | Department of Mathematics, Heze University, Heze, 274015, China |
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| Abstract: | By using Fermat’s method of descent, this paper proved that Diophantine equations { x^{4}-y^{4}=z^{2}} and { x^{4}+4y^{4}=z^{2}} have no non-trivial solutions over {mathbf{Q}}(sqrt{-3}), which implies that the Fermat Equation also has no non-trivial solutions in this field for n =4. |
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| Keywords: | Fermat's method of descent ring of algebraic integers imaginary quadratic fields |
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