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# On the Counting Function of Elliptic Carmichael Numbers

Published:2012-11-13
Printed: Mar 2014
• Florian Luca,
Centro de Ciencias Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, México
• Igor E. Shparlinski,
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
 Format: LaTeX MathJax PDF

## Abstract

We give an upper bound for the number elliptic Carmichael numbers $n \le x$ that have recently been introduced by J. H. Silverman in the case of an elliptic curve without complex multiplication (non CM). We also discuss several possible ways for further improvements.
 Keywords: elliptic Carmichael numbers, applications of sieve methods
 MSC Classifications: 11Y11 - Primality 11N36 - Applications of sieve methods

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