| Diophantine方程x~3-8=py~2解的研究 |
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| 引用本文： | 杨雅琳.Diophantine方程x~3-8=py~2解的研究[J].纺织高校基础科学学报,2010,23(3). |
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| 作者姓名： | 杨雅琳 |
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| 作者单位： | 渭南高级中学,陕西,渭南,714000;西北大学,数学系,陕西,西安,710127 |
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| 摘 要： | 研究丢番图方程正整数解的情况.运用初等方法及同余理论,证明了Diophantine方程x3-8=py2,当p是奇素数且p=3(24k+19)(24k+20)+1,其中k是非负整数,则方程x3-8=py2无正整数解.给出了丢番图方程x3-8=py2无正整数解的一个充要条件.
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| 关 键 词： | Diophantine 方程 正整数解 同余 |
On the Diophantine equation x~3-8=py~2 |
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| YANG YA-lin.On the Diophantine equation x~3-8=py~2[J].Basic Sciences Journal of Textile Universities,2010,23(3). |
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| Authors: | YANG YA-lin |
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| Abstract: | The positive integer solution of the Diophantine equation is studied.Using the elementary and the theory of congruence,Diophantine equation x3-8=py2 is proved,when p is an odd prime,p=3(24k+19)(24k+20)+1 and k is non-negative integer,then the equation has no positive integer solutions.A necessary condition of Diophantine equation x3-8=py2 has no positive integer solutions is given. |
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| Keywords: | Diophantine equation positive integer solution congruence |
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