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

 

Generalized Lucas-Lehmer tests using Pell conics


Author: Samuel A. Hambleton
Journal: Proc. Amer. Math. Soc. 140 (2012), 2653-2661
MSC (2010): Primary 11Y11; Secondary 11G30
Published electronically: December 20, 2011
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Abstract: Pell conics are used to write a Proth-Riesel twin-primality test. We discuss easy-to-find primality certificates for integers of the form $ m^n h \pm 1$. The known primality test for $ 3^n h \pm 1$ is associated with $ X^2+3Y^2 = 4$.


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Additional Information

Samuel A. Hambleton
Affiliation: School of Mathematics and Physics, University of Queensland, St. Lucia, Queensland, Australia 4072
Email: sah@maths.uq.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11196-1
PII: S 0002-9939(2011)11196-1
Keywords: Pell conics, Lucas-Lehmer, primality
Received by editor(s): June 11, 2009
Received by editor(s) in revised form: November 9, 2010, and March 15, 2011
Published electronically: December 20, 2011
Communicated by: Ted Chinburg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.