摘要
Abstract
Using the property of congruence in Number theory,the solutions of Diophantine equation x3±8=Dy2 are in-vestigated,where D is square-free positive integer,D=D1p,D1 cannot exact divided by the prime number 3 or 6k＋1,andpis an positive odd prime.It is proved that if D1=3,7（mod8）,p=3（8k＋7）（8k＋8）＋1,the equation x3＋8=Dy2 hasno positive integer solution,if D1=7（mod8）,p=3（8k＋5）（8k＋6）＋1,the equation x3-8=Dy2 has no positive integersolution.关键词
丢番图方程/正整数解/奇素数Key words
Diophantine equation/positive integer solution/odd prime分类
数理科学
