丢番图方程ax^4+by^4=cz^2的解法

Solution to the Diophantine Equation ax^4+by^4=cz^2

对正整数a,b,c给出了丢番图方程ax4+by4=cz2当(a,b,c)=(2,3,5)时的全部正整数解,结合佟瑞洲关于(a,b,c)=(5,3,2)时方程ax4+by4=cz2的结果,我们给出了丢番图方程ax4+by4=cz2当min{a,b,c}>1且max{a,b,c}≤5时的全部正整数解.从而拓展了Mordell等人关于ax4+by4=cz2的结果.

For positive integer a,b,c,we give all positive integer solutions to the Diophantine equation ax4+by4=cz2 on condition of(a,b,c)=(2,3,5).To combine the result of equation ax4+by4=cz2 with(a,b,c)=(5,3,2) studied by Tong Ruizhou,we give all positive integer solutions to the Diophantine equation ax4+by4=cz2 on condition that min{a,b,c}>1 and max{a,b,c}≤5.Thereby we have developed the result of equation ax4+by4=cz2 studied by Mordell.