| 关于丢番图方程x3-y6=3pz2及其计算程序 |
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| 引用本文： | 王云葵,唐荣保.关于丢番图方程x3-y6=3pz2及其计算程序[J].湖南理工学院学报,2004,17(3):6-10. |
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| 作者姓名： | 王云葵 唐荣保 |
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| 作者单位： | 广西民族学院计算机与信息科学学院 广西南宁530006
(王云葵)，广西灌阳县新桥中学 广西桂林541604(唐荣保) |
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| 摘 要： | 设p≡ 5 (mod6 )为素数 ,证明了丢番图方程x3 -y6=3pz2 在p≡ 5 (mod12 )为素数时均无正整数解 ,在p≡ 11(mod12 )为素数时均有无穷多组正整数解 ,并且还获得了该方程全部正整数解的通解公式 ,同时编写了计算正整数解的计算程序 ,可以很方便地计算该方程的正整数解。
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| 关 键 词： | 丢番图方程 Tijdeman猜想 广义Fermat猜想 计算程序 |
| 文章编号： | 1672-5298(2004)02-0006-05 |
| 修稿时间： | 2004年4月20日 |
On the diophantine equation x3 - y6 = 3pz2 |
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| WANG Yun-kui,TANG Rong-bao.On the diophantine equation x3 - y6 = 3pz2[J].Journal of Hunan Institute of Science and Technology,2004,17(3):6-10. |
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| Authors: | WANG Yun-kui TANG Rong-bao |
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| Abstract: | Supposing p is prime (x 3-y 6=3pz 2), this thesis proved that the diophantine equation had no positive integer solution as well as which is prime. Thesis also proved that the equation had a lot of teams positive integer solution while which was prime, and get the general expressions for all positive integer solutions of the Diophantine Equation. In addition, the thesis designed the computing program for positive integer solutions, to compute the positive integer solutions of this Equation conveniently. |
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| Keywords: | Diophantine equation Tijdeman Suspect Generalization of Fermats Suspect computing program |
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