Translator Disclaimer
2018 The Fibonacci sequence under a modulus: computing all moduli that produce a given period
Alex Dishong, Marc S. Renault
Involve 11(5): 769-774 (2018). DOI: 10.2140/involve.2018.11.769

Abstract

The Fibonacci sequence F=0,1,1,2,3,5,8,13,, when reduced modulo m is periodic. For example, F mod4=0,1,1,2,3,1,0,1,1,2,. The period of F modm is denoted by π(m), so π(4)=6. In this paper we present an algorithm that, given a period k, produces all m such that π(m)=k. For efficiency, the algorithm employs key ideas from a 1963 paper by John Vinson on the period of the Fibonacci sequence. We present output from the algorithm and discuss the results.

Citation

Download Citation

Alex Dishong. Marc S. Renault. "The Fibonacci sequence under a modulus: computing all moduli that produce a given period." Involve 11 (5) 769 - 774, 2018. https://doi.org/10.2140/involve.2018.11.769

Information

Received: 2 June 2016; Accepted: 9 September 2017; Published: 2018
First available in Project Euclid: 12 April 2018

zbMATH: 06866582
MathSciNet: MR3784025
Digital Object Identifier: 10.2140/involve.2018.11.769

Subjects:
Primary: 11B39, 11B50
Secondary: 11Y55

Rights: Copyright © 2018 Mathematical Sciences Publishers

JOURNAL ARTICLE
6 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.11 • No. 5 • 2018
MSP
Back to Top