关于丢番图方x^3-5~3=Dy^2的整数解的研究

On solution to the diophantine equation x^3-5~3=Dy^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丢番图方程x3-53=Dy2无x??0(mod5)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 that the diophantine equation x3-5^3=Dy2 has no integer solutions with x /≡ 0（mod 5）.