Vol. 13, No. 4, 2020

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

Volume 13
Issue 5, 721–900
Issue 4, 541–719
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

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
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.

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