On Fibonacci numbers which are elliptic Carmichael
type: Item
instance of: scholarly article
title: On Fibonacci numbers which are elliptic Carmichael
zbMATH Open document ID: 1389.11048
author: Pantelimon Stanica
author: Florian Luca
published in: Periodica Mathematica Hungarica
publication date: 2017-11-10T00:00:00Z
review text: The concept of an E-Carmichael numbers is introduced in \textit{F. Luca} and \textit{I. E. Shparlinski} [Can. Math. Bull. 57, No. 1, 105--112 (2014; Zbl 1331.11115)]. \smallskip Let \(D = { 2, 3, 7, 11, 19, 43, 67, 163}\), \[ N_d = { n : F_n \text{ is E-Carmichael number related to \(d\)}}, \] and \({F_n}_{n \geq 0}\) be the Finonacci sequence. It is proved the following \textbf{Theorem.} For \(d \in D\): \[ N_d (x) \leq \frac{x}{(log x)^{\frac{1}{2}+o(1)}} (x \rightarrow \infty). \]
Mathematics Subject Classification ID: 11B39
Mathematics Subject Classification ID: 11A51
zbMATH DE Number: 6806092
zbMATH Keywords: Fibonacci numbers
zbMATH Keywords: Elliptic Carmichael numbers
zbMATH Keywords: primitive divisors
reviewed by: Krassimir Atanassov
MaRDI profile type: Publication
full work available at URL: s10998-016-0117-4
OpenAlex ID: W2263578654
cites work: There are infinitely many Carmichael numbers
cites work: Fibonacci numbers at most one away from a perfect power
cites work: On a problem of Oppenheim concerning ''Factorisatio Numerorum''
cites work: Infinitude of elliptic Carmichael numbers
cites work: Q4733903
cites work: The Distribution of Lucas and Elliptic Pseudoprimes
cites work: Q4689684
cites work: Pseudoprime values of the Fibonacci sequence, polynomials and the Euler function
cites work: On the Counting Function of Elliptic Carmichael Numbers
cites work: On the Distribution of Pseudoprimes
cites work: Elliptic Carmichael numbers and elliptic Korselt criteria
cites work: On divisors of Lucas and Lehmer numbers
DOI: 10.1007/S10998-016-0117-4
description: scientific article; zbMATH DE number 6806092