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

 

Cubic reciprocity and generalised Lucas-Lehmer tests for primality of $A.3^n\pm 1$


Authors: Pedro Berrizbeitia and T. G. Berry
Journal: Proc. Amer. Math. Soc. 127 (1999), 1923-1925
MSC (1991): Primary 11A51, 11Y11
Published electronically: February 18, 1999
MathSciNet review: 1487359
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Abstract: Cubic reciprocity is used to derive primality tests analogous to the Lucas-Lehmer test for integers of the form $A.3^n \pm 1$. The test for $A.3^n-1$ is a minor improvement on a test derived by Williams by other means; the test for $A.3^n+1$ seems to be new.


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Additional Information

Pedro Berrizbeitia
Affiliation: Departamento de Matematicas Puras y Aplicadas Universidad Simón Bolívar Caracas, Venezuela
Email: pedrob@usb.ve

T. G. Berry
Affiliation: Departamento de Matematicas Puras y Aplicadas Universidad Simón Bolívar Caracas, Venezuela
Email: berry@usb.ve

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04786-3
PII: S 0002-9939(99)04786-3
Received by editor(s): September 24, 1997
Published electronically: February 18, 1999
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society