关于丢番图方程x^4+my^8=z^2

On the Diophantine Equation

利用数论方法及Fermat无穷递降法 ,获得了丢番图方程x4±my8=z2 与x8±my8=z2 在m=p ,2p ,4p,8p ,16p,32p,6 4p ,12 8p及素数p满足一定条件下无正整数解的充分条件 ,从而完善了Mordell等人的结果 ;

We make use of elementary theory of number and Fermat method of infinite descent so as toobtain somenecessary conditions if the Diophantine equations x 4±my 8=z 2 and x 8±my 8=z 2 have positive Integer solutions that fit (x,y)=1 m.