关于丢番图方程x^3±p^（3n）＝Dy^2

ON THE DIOPHANTINE EQUATIONS x 3±p 3n =Dy 2

对丢番图方程ｘ３±ｐ３ｎ＝Ｄｙ２，ｐ为给定的奇素数，ｐ＝３或ｐ≡５（ｍｏｄ１２），ｎ为自然数，Ｄ＞０，Ｄ无平方因子且不能被６ｋ＋１形的素数整除，现得到该方程非平凡解的关于ｎ的一个递推算法；并给出了ｐ＝３或５，ｎ＝１，２，３。

On the Diophantine equations x 3±p 3n =Dy 2 ,the author has got an algorithm on their nontrivial integer solutions.where p=3 or p≡5( mod 12), p is a prime number, n is a positive integer, D>0 , D is square free and can not divisible by the prime numbers of the form 6k+1 .