| 关于不定方程组y~2-10x~2=9，z~2-17x~2=16 |
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| 引用本文： | 马芙蓉.关于不定方程组y~2-10x~2=9，z~2-17x~2=16[J].四川理工学院学报(自然科学版),2008,21(3). |
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| 作者姓名： | 马芙蓉 |
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| 作者单位： | 重庆师范大学数学与计算机科学学院,重庆,400047 |
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| 摘 要： | 文章运用初等证明方法,证明了标题所述的不定方程组只有x=0的整数解。从而证明了只有一个整数N=1使得1,10,17,N的任意两数之积减去1后均为平方数。
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| 关 键 词： | 不定方程组 整数解 P_(-1)集 扩张 |
On the System of Diophantine Equations y2-10x2=9 and z2-17x2=16 |
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| MA Fu-rong.On the System of Diophantine Equations y2-10x2=9 and z2-17x2=16[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2008,21(3). |
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| Authors: | MA Fu-rong |
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| Abstract: | In this paper,it has proved that the system of diophantine equations y~2-10x~2=9 and z~2-17x~2=16 has only integer solution x=0 by using the elementary methods.In other words, N=1 is the only integer such that the product of any two of 1,10,17,decreased by 1 is a perfect square. |
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| Keywords: | the system of diophantine equations integer solution P_(-1) sots extension |
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