Anomalous primes and the elliptic Korselt criterion

L. Babinkostova; J. C. Bahr; Y. H. Kim; E. Neyman; G. K. Taylor

doi:10.1016/j.jnt.2019.02.013

Anomalous primes and the elliptic Korselt criterion

L. Babinkostova, J. C. Bahr, Y. H. Kim, E. Neyman, G. K. Taylor

Mathematics Department

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We explore the relationship between elliptic Korselt numbers of Type I, a class of pseudoprimes introduced by Silverman in [10], and anomalous primes. We generalize a result in [10] that gives sufficient conditions for an elliptic Korselt number of Type I to be a product of anomalous primes. Finally, we prove that almost all elliptic Korselt numbers of Type I of the form n=pq are a product of anomalous primes.

Original language	English
Pages (from-to)	108-123
Number of pages	16
Journal	Journal of Number Theory
Volume	201
DOIs	https://doi.org/10.1016/j.jnt.2019.02.013
State	Published - Aug 2019

Keywords

Anomalous primes
Elliptic Korselt numbers
Elliptic curves

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10.1016/j.jnt.2019.02.013

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title = "Anomalous primes and the elliptic Korselt criterion",

abstract = "We explore the relationship between elliptic Korselt numbers of Type I, a class of pseudoprimes introduced by Silverman in [10], and anomalous primes. We generalize a result in [10] that gives sufficient conditions for an elliptic Korselt number of Type I to be a product of anomalous primes. Finally, we prove that almost all elliptic Korselt numbers of Type I of the form n=pq are a product of anomalous primes.",

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AU - Bahr, J. C.

AU - Kim, Y. H.

AU - Neyman, E.

AU - Taylor, G. K.

PY - 2019/8

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N2 - We explore the relationship between elliptic Korselt numbers of Type I, a class of pseudoprimes introduced by Silverman in [10], and anomalous primes. We generalize a result in [10] that gives sufficient conditions for an elliptic Korselt number of Type I to be a product of anomalous primes. Finally, we prove that almost all elliptic Korselt numbers of Type I of the form n=pq are a product of anomalous primes.

AB - We explore the relationship between elliptic Korselt numbers of Type I, a class of pseudoprimes introduced by Silverman in [10], and anomalous primes. We generalize a result in [10] that gives sufficient conditions for an elliptic Korselt number of Type I to be a product of anomalous primes. Finally, we prove that almost all elliptic Korselt numbers of Type I of the form n=pq are a product of anomalous primes.

KW - Anomalous primes

KW - Elliptic Korselt numbers

KW - Elliptic curves

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JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Anomalous primes and the elliptic Korselt criterion

Abstract

Keywords

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