重庆工商大学学报：自然科学版2012，Vol.29Issue(9)：5-7,28,4.
关于Pell方程px~2-（pn±2）y~2=±1（p≡-1,±3（mod8）是素数）
On Pell Equation px~2-（pn±2）y~2=±1（p≡-1,±3（mod8）,p is a prime factor）
摘要
Abstract
The solubility of Pell equation ax2-by2=±1（a,b∈Z＋,ab is a non-square positive integer）is a very meaningful question.In this paper,by applying related knowledge of Legendre sign and nature of congruence,it works out six conclusions to judge that the sets of Pell equations such as px2-（pn±2）y2=±1（p≡-1,±3（mod 8）,and p is a prime number） have not positive integer solutions.These conclusions play an important role in the research on restricted Pell equation x2-Dy2=±1（D is a non-square positive integer）.关键词
Pell方程/正整数解/素数/同余Key words
Pell Equation/positive integer solution/prime number/congruence分类
数理科学引用本文复制引用
杜先存,黄梅,赵金娥..关于Pell方程px~2-（pn±2）y~2=±1（p≡-1,±3（mod8）是素数）[J].重庆工商大学学报：自然科学版,2012,29(9):5-7,28,4.基金项目
云南省教育厅科研基金（2011C121）. （）
