Table of Contents
ISRN Algebra
Volume 2014 (2014), Article ID 750325, 5 pages
http://dx.doi.org/10.1155/2014/750325
Research Article

Divisibility Properties of the Fibonacci, Lucas, and Related Sequences

Department of Mathematics and Statistics, University of Guelph, Guelph, ON, Canada N1G 2W1

Received 13 December 2013; Accepted 22 January 2014; Published 4 March 2014

Academic Editors: H. Airault and W. Gao

Copyright © 2014 Thomas Jeffery and Rajesh Pereira. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use matrix techniques to give simple proofs of known divisibility properties of the Fibonacci, Lucas, generalized Lucas, and Gaussian Fibonacci numbers. Our derivations use the fact that products of diagonal matrices are diagonal together with Bezout’s identity.