关于丢番图方程px^4-(p-4)y^2=4z^2

On Diophantine Equation px^4-(p-4)y^2=4z^2

利用初等方法给出了丢番图方程px4-(p-4)y2=4z2当p=q Q2+4,q≡3(mod 4),p、q为奇素数时的全部正整数解,从而拓展了Mordell等学者关于ax4+by4=cz2的结果。

When p=qQ2＋4,q≡3（mod 4）, withp,q odd prime, we give all positive integer solutions to the Diophantine equationpx4-（p-4）y2=4z2 by the elementary methods. Thereby we have extended the result of equationax4＋by4=cz2 studied by Mordell etc.