关于丢番图方程px^4-qy^2=z^4

On Diophantine Equation px^4-qy^2=z^4

利用初等方法把丢番图方程px4-qy2=z4化为方程x2+my2=z2,给出了方程px4-qy2=z4当p=2Q2+1,Q>0,q=2,p为奇素数时的全部正整数解。利用这一方法可以解决一类方程px4-qy2=z4的求解问题,从而拓展了关于px4-qy2=z4的结果。

Px4-qy2=z4 is changed into x2＋my2=z2 by using elementary methods. When p=2Q2＋l, Q 〉 0, q=2, p is odd prime integer, then all positive integer solutions of diophantine equation px4-qy2=z4are given. The foregoing method may be used to solve a class of equations such as px4,qy2=z4 and the result of equationpx4-qy2=4 are developed hereof.