Splitting Fields and Periods of Fibonacci Sequences Modulo Primes

Authors

Sanjai Gupta, Irvine Valley College
Parousia Rockstroh '08, Harvey Mudd CollegeFollow
Francis E. Su, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article

Department

Mathematics (HMC)

Publication Date

4-2012

Abstract

We consider the period of a Fibonacci sequence modulo a prime and provide an accessible, motivated treatment of this classical topic using only ideas from linear and abstract algebra. Our methods extend to general recurrences with prime moduli and provide some new insights. And our treatment highlights a nice application of the use of splitting fields that might be suitable to present in an undergraduate course in abstract algebra or Galois theory.

Comments

Archived with permission from the Mathematical Association of America

Rights Information

© 2012 Mathematical Association of America

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.4169/math.mag.85.2.130

Recommended Citation

Sanjai Gupta, Parousia Rockstroh, and Francis Edward Su. Splitting fields and periods of Fibonacci sequences modulo primes. Math. Mag., Volume 85, Number 2, April 2012, 130-135.