THE FIBONACCI SEQUENCE MODULO p 2 – AN INVESTIGATION BY COMPUTER FOR

@inproceedings{Elsenhans2006THEFS,
  title={THE FIBONACCI SEQUENCE MODULO p 2 – AN INVESTIGATION BY COMPUTER FOR},
  author={Andreas-Stephan Elsenhans and J{\"o}rg Jahnel},
  year={2006}
}
We show that for primes p < 10 the period length κ(p) of the Fibonacci sequence modulo p is never equal to its period length modulo p. The investigation involves an extensive search by computer. As an application, we establish the general formula κ(p) = κ(p) · pn−1 for all primes less than 10. 

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-8 of 8 references

Algorithmische Zahlentheorie (Algorithmic number

  • O. Fo Forster
  • 1996

A course in computational algebraic number theory, Springer, Graduate Texts Math

  • H. Cohen
  • 1993

A classical introduction to modern number theory, Second edition, Springer, Graduate Texts Math

  • K. Ireland, M. Rosen
  • 1990

Modular multiplication without trial

  • P. L. Mo Montgomery
  • division, Math. Comp
  • 1985

Über die mittlere Periodenlänge der Fibonacci-Folgen modulo p (On the average period length of the Fibonacci sequences modulo p), Dissertation, Fakultät für Math. und Nat.-Wiss

  • G. Gö Göttsch
  • 1982

Approximate formulas for some functions of prime numbers, Illinois

  • J. B. Rosser, L. Schoenfeld
  • J. Math
  • 1962

Fibonacci series modulo m

  • D. D. Wa Wall
  • Amer. Math. Monthly
  • 1960

Two theorems on Fibonacci’s

  • D. Ja Jarden
  • sequence, Amer. Math. Monthly
  • 1946