关于丢番图方程px^4-(p-1)y^2=z^4

On the Diophantine Equation px^4-(p-1)y^2=z^4

利用初等方法给出了丢番图方程px4-(p-1)y2=z4当p=qQ2+1,2|Q,q≡3(mod4),p、q为奇素数时的全部正整数解,从而拓展了王洪昌和王春光的px4-(p-1)y2=z4的结果.

we give all positive integer solutions to the diophantine equation px^4-（p-1）y^2=z^4 by the elementary methods on condition that p=qQ^2＋1,2｜Q,q≡3（mod 4）,p and q are odd prime number.Thereby we have extended the result of equation px^4-（p-1）y^2=z^4 studied by Wang Hongchang and Wang Chunguang.