Pseudoprime reductions of elliptic curves

Alina Carmen Cojocaru*, Florian Luca, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
1 Downloads (Pure)

Abstract

Let b ≥ 2 be an integer and let E/ q be a fixed elliptic curve. In this paper, we estimate the number of primes p ≤ x such that the number of points nE(p) on the reduction of E modulo p is a base b prime or pseudoprime. In particular, we improve previously known bounds which applied only to prime values of nE(p).

Original languageEnglish
Pages (from-to)513-522
Number of pages10
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume146
Issue number3
DOIs
Publication statusPublished - May 2009

Bibliographical note

Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Corrigendum can be found in Mathematical Proceedings of the Cambridge Philosophical Society, Volume 152(3), 571, http://dx.doi.org/10.1017/S0305004111000399.

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