| 一个Diophantine方程组 |
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| 引用本文： | 乐茂华. 一个Diophantine方程组[J]. 黑龙江大学自然科学学报, 2004, 21(1): 11-16 |
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| 作者姓名： | 乐茂华 |
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| 作者单位： | 湛江师范学院,数学系,广东,湛江,524048 |
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| 基金项目： | Supported by the National Natural Science Foundation of China(10271104)，the Guangdong Provincial Natural Science Foundation(011781)，the Natural Science Foundation of the Education Department of Guangdong Province(0161) |
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| 摘 要： | 设D是正整数.1995年,M.Mignotte和A.Petho运用深奥的超越数论方法确定了方程组x2-Dy2=1-D和x=2z2-1在D=6时的全部正整数解(x,y,z).对于D-1是奇素数方幂这个一般情况,给出了确定该方程组全部正整数解的初等方法,并且由此找出了该方程组在D=6和8时的全部正整数解.
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| 关 键 词： | Diophantine方程组 四次方程 初等方法 |
On the Diophantine system x2- Dy2= 1-D and x2= 2z2- 1 |
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| Abstract. On the Diophantine system x2- Dy2= 1-D and x2= 2z2- 1[J]. Journal of Natural Science of Heilongjiang University, 2004, 21(1): 11-16 |
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| Authors: | Abstract |
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| Abstract: | Let D be a positive integer. In 1995, M. Mignotte and A. Petho determined all positive integer solutions (x, y, z) of equations x2 - Dy2=1- D and x = 2z2-1 for D = 6. Their proof relied upon deep tools of transcendence number theory. An elementary method is given to find all positive integer solutions of the equations for the general case that D - 1 is an odd prime power. As a consequence, all positive integer solutions of the equations for D = 6 and 8 are determined. |
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| Keywords: | Diophantine system quartic equation elementary method |
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