摘要
在素数p=3(8t+4)(8t+5)+1和p=3(8t+3)(8t+4)+1的情形下,运用初等数论的方法给出了丢番图方程x3+1=py2无正整数解的充分条件,并得到无数个6k+1型的素数p使得方程x3+1=py2无正整数解.
Using elementary theory of numbers methods,a sufficient condition is obtained that the Diophantine equation x3＋1 = py2 has no positive integer solution,where p = 3（8t＋4）（8t＋5）＋1 and p = 3（8t＋3）（8t＋4）＋1.And get countless p,where p is an odd prime of the form 6k＋1,meet the equation x3＋1 = py2 without positive integer solution.
出处
《纯粹数学与应用数学》
CSCD
2010年第4期687-690,共4页
Pure and Applied Mathematics
关键词
丢番图方程
正整数解
奇素数
同余
Diophantine equation
positive integer solution
odd prime
recurrent sequent
