Vol. 13, No. 4, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 3, 361–540
Issue 2, 181–360
Issue 1, 1–179

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Polynomial values in Fibonacci sequences

Adi Ostrov, Danny Neftin, Avi Berman and Reyad A. Elrazik

Vol. 13 (2020), No. 4, 597–605
Abstract

The only perfect powers in the Fibonacci sequence are 0, 1, 8, and 144, and in the Lucas sequence, the only perfect powers are 1 and 4. We prove that in sequences that follow the same recurrence relation of the Lucas and Fibonacci sequences, there are always only finitely many polynomial values g() for any polynomial g which is not equivalent to a Dickson polynomial.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/involve

We have not been able to recognize your IP address 3.215.177.171 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

Keywords
recurrence sequence, polynomial values, Fibonacci
Mathematical Subject Classification 2010
Primary: 11B39, 11C08
Milestones
Received: 14 December 2019
Revised: 21 April 2020
Accepted: 26 July 2020
Published: 20 November 2020

Communicated by Kenneth S. Berenhaut
Authors
Adi Ostrov
Department of Mathematics
Technion – Israel Institute of Technology
Haifa
Israel
Danny Neftin
Department of Mathematics
Technion – Israel Institute of Technology
Haifa
Israel
Avi Berman
Department of Mathematics
Technion – Israel Institute of Technology
Haifa
Israel
Reyad A. Elrazik
Department of Mathematics
Technion – Israel Institute of Technology
Haifa
Israel