Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On the number of solutions of $x^2-4m(m+1)y^2=y^2-bz^2=1$

Author: Pingzhi Yuan
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1561-1566
MSC (2000): Primary 11D09; Secondary 11D25
Published electronically: January 20, 2004
MathSciNet review: 2051114
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, using a result of Ljunggren and some results on primitive prime factors of Lucas sequences of the first kind, we prove the following results by an elementary argument: if $m$ and $b$ are positive integers, then the simultaneous Pell equations


possesses at most one solution $(x,y,z)$ in positive integers.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11D09, 11D25

Retrieve articles in all journals with MSC (2000): 11D09, 11D25

Additional Information

Pingzhi Yuan
Affiliation: Department of Mathematics, Zhongshan University, Guangzhou 510275, P.R. China

PII: S 0002-9939(04)07418-0
Keywords: Simultaneous Diophantine equations, Pell equations, Lucas sequences
Received by editor(s): September 3, 2002
Published electronically: January 20, 2004
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2004 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia