中文摘要：

设p是6k＋1型的奇素数，探讨了Diophantine方程x^3 -1=3 py^2的正整数解的情况。运用Pell方程px^2 -3 y^2=1的最小解、同余式、平方剩余、勒让德符号等初等方法证明了两个结论。

英文摘要：

The positive integer solutions of the Diophantine equation x3-1= 23 py are studied on condition that p is an odd prime of the form 6k＋1 . By using the elementary method of the minimal solution of the Pell equation 2px -3 y 2 =1 , congruent formula, quadratic residue and Legendre symbol, two related conclusions are proved.