关于丢番图方程x^3±5~3=3py^2的整数解

On the Diophantine Equation x^3±5~3=3py^2

设p为奇素数,运用同余式、平方剩余等初等方法得出了丢番图方程x3±53=3py2无正整数解的两个充分条件.

Let p be an odd prime.By using congruent formula and quadratic residue,two sufficient con-ditions are obtained that the Diophantine equation x3 ± 53 =3py2 hasno positive integer solutions.