| 关于Diophantine方程x^3-1=3py^2 |
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| 引用本文： | 万 飞,杜先存.关于Diophantine方程x^3-1=3py^2[J].唐山师范学院学报,2014(2):14-15. |
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| 作者姓名： | 万 飞 杜先存 |
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| 作者单位： | 红河学院教师教育学院,云南蒙自661199 |
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| 基金项目： | 云南省教育厅科研基金（2012C199）,江苏省教育科学“十二五”规划课题项目（D201301083） |
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| 摘 要： | 设p是6k＋1型的奇素数，探讨了Diophantine方程x^3 -1=3 py^2的正整数解的情况。运用Pell方程px^2 -3 y^2=1的最小解、同余式、平方剩余、勒让德符号等初等方法证明了两个结论。
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| 关 键 词： | Diophantine方程 奇素数 最小解 正整数解 勒让德符号 |
On the Diophantine Equation x3-1=3py2 |
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| WAN Fei,DU Xian-cun.On the Diophantine Equation x3-1=3py2[J].Journal of Tangshan Teachers College,2014(2):14-15. |
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| Authors: | WAN Fei DU Xian-cun |
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| Institution: | (Teachers＇ Educational College, Honghe University, Mengzi 661199, China) |
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| Abstract: | The positive integer solutions of the Diophantine equation x3-1= 23 py are studied on condition that p is an odd prime of the form 6k＋1 . By using the elementary method of the minimal solution of the Pell equation 2px -3 y 2 =1 , congruent formula, quadratic residue and Legendre symbol, two related conclusions are proved. |
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| Keywords: | Diophantine equation odd prime minimal solution positive integer solution Legendre symbol |
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