关于指数丢番图方程x^3+1=py^2与x^3+1=3py^2

On the Exponent Diophantine Equation x^3+1=py^2 and x^3+1=3py^2

设p是6k+1型的奇素数,运用初等方法给出了当p=3n(n+1)+1(n∈N),且3(2n+1)时指数丢番图方程x3+1=py2与x3+1=3py2无正整数解的充分条件.

Let p be an odd prime of the form 6k ＋ 1.Using elementary method,the sufficient condition was obtained that the exponent Diophantine equation x3 ＋ 1 = py2 and x3 ＋ 1 = 3py2 have no integer solutions,where p = 3n（n ＋1） ＋1（n∈N）,and 3（2n ＋1）.