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A primality test for $ Kp^n+1$ numbers

Authors: José María Grau, Antonio M. Oller-Marcén and Daniel Sadornil
Journal: Math. Comp. 84 (2015), 505-512
MSC (2010): Primary 11Y11, 11Y16, 11A51, 11B99
Published electronically: June 10, 2014
MathSciNet review: 3266973
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Abstract: In this paper we generalize the classical Proth's theorem and the Miller-Rabin test for integers of the form $ N=Kp^n+1$. For these families, we present variations on the classical Pocklington's results and, in particular, a primality test whose computational complexity is $ \widetilde {O}(\log ^2 N)$ and, what is more important, that requires only one modular exponentiation modulo $ N$ similar to that of Fermat's test.

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José María Grau
Affiliation: Departamento de Matemáticas, Universidad de Oviedo, Avda. Calvo Sotelo, s/n, 33007 Oviedo, Spain

Antonio M. Oller-Marcén
Affiliation: Centro Universitario de la Defensa de Zaragoza, Ctra. de Huesca, s/n, 50090 Zaragoza, Spain

Daniel Sadornil
Affiliation: Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, F. Ciencias, Avda de los Castros s/n, 39005 Santander, Spain

Received by editor(s): June 12, 2012
Received by editor(s) in revised form: May 13, 2013
Published electronically: June 10, 2014
Additional Notes: Daniel Sadornil was partially supported by the Spanish Government under projects MTM2010-21580-C02-02 and MTM2010-16051.
Article copyright: © Copyright 2014 American Mathematical Society

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