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On the Counting Function of Elliptic Carmichael Numbers

Published online by Cambridge University Press:  20 November 2018

Florian Luca  and
Igor E. Shparlinski
Florian Luca
Affiliation:
Centro de Ciencias Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, Máxico e-mail: fluca@matmor.unam.mx
Igor E. Shparlinski
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia e-mail: igor.shparlinski@mq.edu.au
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Abstract

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We give an upper bound for the number of elliptic Carmichael numbers $n\,\le \,x$ that were recently introduced by J. H. Silverman in the case of an elliptic curve without complex multiplication (non $\text{CM}$). We also discuss several possible further improvements.

Keywords

11Y1111N36elliptic Carmichael numbersapplications of sieve methods
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 1 , 14 March 2014 , pp. 105 - 112
Copyright
Copyright © Canadian Mathematical Society 2014

References

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