Anomalous primes and the elliptic Korselt criterion

被引：4

作者：

Babinkostova, L. ^{[1
]}

Bahr, J. C. ^{[2
]}

Kim, Y. H. ^{[3
]}

Neyman, E. ^{[4
]}

Taylor, G. K. ^{[5
]}

机构：

[1] Boise State Univ, Dept Math, Boise, ID 83725 USA

[2] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[3] Columbia Univ, Dept Math, New York, NY 10027 USA

[4] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[5] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

来源：

JOURNAL OF NUMBER THEORY | 2019年 / 201卷

基金：

美国国家科学基金会;

关键词：

Elliptic curves; Anomalous primes; Elliptic Korselt numbers;

D O I：

10.1016/j.jnt.2019.02.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：108 / 123

页数：16

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