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.
© 2012 Mathematical Association of America
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.