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On the Solutions of the Pell Equation x2-2y2=1 and y2-Dz2=4(PDF)

《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

Issue:
2014年03期
Page:
44-
Research Field:
数学
Publishing date:

Info

Title:
On the Solutions of the Pell Equation x2-2y2=1 and y2-Dz2=4
Author(s):
Ren Xiaozhi
School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China
Keywords:
Pell equationcommon solutiontrivial solution
PACS:
O156
DOI:
-
Abstract:
In this paper,the following conclusion is proved:If D-1(mod 12)and D>0 is an odd squarefree integer which has 7 or 8 distinct prime factors,the equation x2-2y2=1 and y-Dz2=4 has only one trivial solution z=0.

References:

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[2]陈建华.关于Pell方程组x2-2y2=1和y2-Dz2=4的公解[J].武汉大学学报:自然科学版,1990,36(1):8-12.
[3]陈永高.关于Pell方程组x2-2y2=1和y2-Dz2=4的公解[J].北京大学学报:自然科学版,1994,30(3):298-302.
[4]马德刚.方程6y2=x(x+1)(2x+1)的公解[J].北京大学学报:自然科学版,1994,30(3):298-302.
[4]马德刚.方程初等证明[J].四川大学学报:自然科学版,1985,22(4):107-116.

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Last Update: 2014-09-30