关于丢番图方程x^4+dy^4=z^2

On the Diophantine Equation x^4+dy^4=z^2

利用分解法和无穷递降法研究了一类丢番图方程的解,结果证明了丢番图方程x4+dy4=z2,gcd(x,y)=1,这里d为整数且d≠0,在d=3n及n≡3(mod4)时,无正整数解。

Using decomposition method and method of infinite descent,the author considers a class of Diophantine equations.In this paper,we prove the Diophantine equation x4+dy4=z2,with gcd(x,y)=1,and provethat if d=3n and n≡3(mod4),then it has no positive integer solution.