| 关于Diophantine方程x3+1=py2 |
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| 引用本文： | 高洁,袁进. 关于Diophantine方程x3+1=py2[J]. 纯粹数学与应用数学, 2010, 26(4): 687-690. DOI: 10.3969/j.issn.1008-5513.2010.04.027 |
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| 作者姓名： | 高洁 袁进 |
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| 作者单位： | 西北大学数学系,陕西,西安,710127;西北大学数学系,陕西,西安,710127 |
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| 摘 要： | 在素数p=3（8t＋4）（8t＋5）＋1和p=3（8t＋3）（8t＋4）＋1的情形下,运用初等数论的方法给出了丢番图方程x3＋1=py2无正整数解的充分条件,并得到无数个6k＋1型的素数p使得方程x3＋1=py2无正整数解.
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| 关 键 词： | 丢番图方程 正整数解 奇素数 同余 |
On the Diophantine equation x3 + 1 =py2 |
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| GAO Jie,YUAN Jin. On the Diophantine equation x3 + 1 =py2[J]. Pure and Applied Mathematics, 2010, 26(4): 687-690. DOI: 10.3969/j.issn.1008-5513.2010.04.027 |
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| Authors: | GAO Jie YUAN Jin |
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| Affiliation: | GAO Jie 1,YUAN Jin 2(Department of Mathematics,Northwest University,Xi'an 710127,China) |
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| Abstract: | Using elementary theory of numbers methods,a sufficient condition is obtained that the Diophantine equation x3+1 = py2 has no positive integer solution,where p = 3(8t+4)(8t+5)+1 and p = 3(8t+3)(8t+4)+1.And get countless p,where p is an odd prime of the form 6k+1,meet the equation x3+1 = py2 without positive integer solution. |
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| Keywords: | Diophantine equation positive integer solution odd prime recurrent sequent |
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