关于丢番图方程X^2=Dy^4+4

On the Diophantine Equation x^2 = Dy^4 + 4

本文用初等方法研究了Diophantine equation x^2＝Dy^4+4, D〉0且不是平方数,无正整数解的充分条件问题,得到了与Cohn^(1-3)的结果不同的另一些结果.

Abstract In this paper, we give, by elementary methods, some sufficiency coditions that diophantine equation x2 = Dy4+ 4(D> 0 ), and is not perfect square) has no positive integer solutions. And we get some other results different from Cohn[1]-[3].