Splitting fields and periods of Fibonacci sequences modulo primes

Details Splitting fields and periods of Fibonacci sequences modulo primes Splitting fields and periods of Fibonacci sequences modulo primes

2009-09-02

arxiv.org/abs/0909.0362v1

Mathematics

Number Theory

5 pages. See also http://www.math.hmc.edu/~su/papers.html

Scientific paper

What is the period of the Fibonacci sequence modulo a prime? The purpose of our brief expository paper is to illustrate an accessible, motivated treatment of this classical topic using only ideas from linear and abstract algebra (rather than the case-by-case analysis found in many papers on the subject, or techniques from graduate number theory). 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 undergraduate course in abstract algebra or Galois theory.

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