On the Counting Function of Elliptic Carmichael Numbers

TL;DR

This paper establishes an upper bound on the count of elliptic Carmichael numbers up to a certain limit, providing insights into their distribution and suggesting avenues for future research.

Contribution

It introduces an upper bound for elliptic Carmichael numbers and explores potential methods for improving this bound.

Findings

Established an upper bound for elliptic Carmichael numbers up to x.

Discussed possible approaches for tightening the bound.

Contributed to understanding the distribution of elliptic Carmichael numbers.

Abstract

We give an upper bound for the number elliptic Carmichael numbers $n \le x$ that have recently been introduced by J. H. Silverman. We also discuss several possible ways for further improvements.