The 99th Fibonacci Identity

Authors

Arthur T. Benjamin, Harvey Mudd CollegeFollow
Alex K. Eustis '06, Harvey Mudd CollegeFollow
Sean S. Plott '08, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

2-25-2008

Abstract

We provide elementary combinatorial proofs of several Fibonacci and Lucas number identities left open in the book Proofs That Really Count [1], and generalize these to Gibonacci sequences G_n that satisfy the Fibonacci recurrence, but with arbitrary real initial conditions. We offer several new identities as well.

[1] A. T. Benjamin and J. J. Quinn, Proofs That Really Count: The Art of Combinatorial Proof, The Dolciani Mathematical Expositions, 27, Mathematical Association of America, Washington, DC, 2003

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,452.

First published in the Electronic Journal of Combinatorics, vol. 15, no. 1 (2008).

Publisher pdf, posted with permission.

Rights Information

© 2008 The Electronic Journal of Combinatorics

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Benjamin, Arthur, Alex Eustis, and Sean Plott. "The 99th Fibonacci Identity." The Electronic Journal of Combinatorics 15.1 (2008).