| 摘要: |
| 设p为素数,利用Fermat无穷递降法,研究方程x4±3px2y2+3p2y4=z2与x4±6px2y2±3p2y4=z2正整数解的存在性,证明该方程在p≡5(mod 12)时均无正整数解,在p≡11(mod 12)时有解且有无穷多组正整数解,获得方程无穷多组正整数解的通解公式和方程的部分正整数解. |
| 关键词: 丢番图方程 Fermat无穷递降法 正整数解 |
| DOI： |
| 投稿时间：2005-05-11修订日期：2005-08-04 |
| 基金项目:广西壮族自治区教育厅科研项目资助(广义Fermat猜想的研究). |
|
| On the Diophantine Equation x4±6px2y2±3p2y4=z2 |
|
Zhou Ke
|
| (Department of Mathematics and Computer Science, Guangxi Teacher's Education. University, Nanning, Guangxi, 530001, China) |
| Abstract: |
| Let p be a prime number,using Fermat Infinite method of descent,to study the positive integral solution of the equations x4±3px2y2+3p2y4=z2 and x4±6px2y2±3p2y4=z2.Proved that the equations have no positive integer solution were proved,where p≡5(mod 12).They have infinite multi-groups positive integer solution while p≡11(mod 12).The infinite multi-group positive integer solution formula and a part for positive integer solution of the equations have been given. |
| Key words: Diophtine equation Fermat infinite method of descent positive integral solution |
