摘要
证明了丢番图方程x3 +y3 =Dz4 ,(x,y) =1在D =1,2,3,4,6,8,12,18,2 4,2 7,3 6,54,72,10 8,2 16时仅有xyz≠ 0的整数解(D,x,y,z)=(2,1,1,± 1),同时猜想方程x3 + y3 =9z4 仅有xyz≠ 0的整数解(x,y,z)=(1,2,± 1),(71,-2 3,± 14)
We make use of elementary theory of number and Fermat method of infinite descent, shows that the diophantine equations x 8-4y 4=pz 4,x 4-4y 8=pz 8 and 64x 8±y 4=pz 4 have no positive integer solutions when (x,y)=1; the diophantine equation x 4+4y 8=pz 4 in the title has a positive integer solution only if p=5, x=y=z=1.In the same way,x 8+my 4=z 4 can have a solution if m=±p,±2p,±4p,±8p.
出处
《广西民族学院学报（自然科学版）》
CAS
2001年第3期161-164,共4页
Journal of Guangxi University For Nationalities(Natural Science Edition)
基金
广西民族学院重点科研项目资助课题(0 0SXX0 0 0 0 2)
关键词
三次丢番图方程
丢番图方程
整数解
Diophantine equations
Fermat method of infinite descent
Positive integer solutions
