| 关于丢番图方程x3-1=py2 |
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| 引用本文： | 何桃,郭金保,穆秀梅,赵杏花.关于丢番图方程x3-1=py2[J].河南科学,2011,29(12):1421-1422. |
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| 作者姓名： | 何桃 郭金保 穆秀梅 赵杏花 |
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| 作者单位： | 延安大学数学与计算机科学学院,陕西 延安,716000 |
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| 摘 要： | 设s为正整数且2｜s,素数p=27s2+1,利用初等方法证明了丢番图方程x3-1=py2仅有平凡整数解(x,y)=(1,0).
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| 关 键 词： | 丢番图方程 整数解 平凡整数解 |
On the Diophantine Equation x3-1=py2 |
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| He Tao
,
Guo Jinbao
,
Mu Xiumei
,
Zhao Xinhua.On the Diophantine Equation x3-1=py2[J].Henan Science,2011,29(12):1421-1422. |
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| Authors: | He Tao Guo Jinbao Mu Xiumei Zhao Xinhua |
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| Institution: | He Tao, Guo Jinbao, Mu Xiumei, Zhao Xinhua (College of Mathematics and Computer Science, Yah＇an University, Yan＇an 716000, Shaanxi China) |
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| Abstract: | Let p be an odd prime, by using the elementary method, this paper proved that if p=27s2＋1, where s is an even integer then the Diophantine equation, x3-1 =py2, has only one solution （x, y）= （1,0）. |
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| Keywords: | Diophantine equation positive integer solution trivial integer solution |
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