关于Diophantine方程x^3-5~3=2Dy^2的整数解

On the Solution of the Diophantine Equation x^3-5~3= 2Dy^2

设D为奇素数,运用平方剩余、同余式、乐让德符号的性质等初等方法得出了Diophantine方程x3-53=2Dy2无x≠0(mod 5)的正整数解的两个充分条件.

Let D be an odd prime. By using quadratic residue, congruent formula and legendre symbol, two sufficient conditions are obtained when the Diophantine equation x^3-5^3=2Dy^2 has no integer solutions with x≠0（ mod 5）.