关于丢番图方程x^4±6px^2y^2±3p^2y^4=z^2  

On the Diophantine Equation x^4±6px^2y^2±3p^2y^4=z^2

作　　者：周科[1] 

机构地区：[1]广西师范学院数学与计算机科学系,广西南宁530001

出　　处：《广西科学》2005年第4期255-258,共4页Guangxi Sciences

基　　金：广西壮族自治区教育厅科研项目资助(广义Fermat猜想的研究)

摘　　要：设p为素数,利用F erm at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(m od 12)时均无正整数解,在p≡11(m od 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.Let p be a prime number, using Fermat Infinite method of descent, to study the positive integral solution of the equations x^4±3px^2y^2＋3p^2y^4=z^2 and x^4±6px^2y^2±3p^2y^4=z^2. Proved that the equations have no positive integer solution were proved,where p ≡5 （mod12）. They have infinite multi-groups positive integer solution while p ≡ 11 （rood 12）. The infinite multi-group positive integer solution formula and a part for positive integer solution of the equations have been given.

关 键 词：丢番图方程 FERMAT无穷递降法 正整数解 

分 类 号：O156.7[理学—数学]