关于丢番图方程px^4-(p-2)y^2=2z^4

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

利用初等方法给出了丢番图方程px4-(p-2)y2=2z4当p=Q2+2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=Q^2＋2, p is odd prime, we give all positive integer solutions to the Diophantine equation px^4- （p-2）y^2= 2z4 by the elementary methods. Thereby we expanded the result of equation ax^4by^4cz^2 which was studied by Mordell etc.