摘要
利用数论方法及Fermat无穷递降法 ,证明了丢番图方程x4+my4=nz2 在 (m ,n) =(- 18,1) ,(72 ,1) ,(12 ,1) ,(36 ,1) ,(- 2 7,1) ,(± 10 8,1) ,(- 2 7,- 2 ) ,(- 4,- 2 7) ,(6 ,1) ,(- 2 4,1) ,(2 ,1) ,(- 8,1)时均无正整数解 ;在 (m ,n) =(- 4,- 3)和 (- 9,- 8)时均只有正整数解x =y =z=1,从而解决了Mordell和曹珍富遗留的难题。
In this paper,it is proved that the Diophantine equation x 4+my 4=nz 2 has no pisitive integer solution when (m,n)=(-18,1),(72,1),(12,1),(36,1),(-27,1),(±108,1),(-27,-2),(-4,-27),(6,1),(-24,1),(2,1),(-8,1),and has only the pisitive integer solution x=y=z=1 when (m,n)=(-4,-3) and (-9,-8) with elementary theory of number,so the diffical problems left by Mordell and Cao Cenfu have been solved.
出处
《广西师院学报（自然科学版）》
2001年第2期13-18,共6页
Journal of Guangxi Teachers College(Natural Science Edition)
