Fibonacci numbers with modular rings

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 4, 1998, Number 4, Pages 165–174
Full paper (PDF, 6568 Kb)

Details

Authors and affiliations

J. V. Leyendekkers
The University of Sydney, 2006, Australia

A. G. Shannon
University of Technology, Sydney, 2007, Australia

AMS Classification

  • 11R29
  • 11B39

References

  1. Barakat, Richard. 1964. The matrix operator ezand the Lucas polynomials. Journal of Mathematics and Physics. 43: 332-335.
  2. Brent, R P. 1994. On the periods of generalized Fibonacci recurrences. Mathematics of Computation. 63: 207.
  3. Carlitz, L. 1955. Some class number relations. Mathematische Zeitschrift. 62: 167-170.
  4. D’Antona Ottavio, M. 1998. The would-be method of targeted rings, in Bruce Sagan & Richard P Stanley (eds). Mathematical Essay’s in Honor of Gian-Carlo Rota. Boston: Birkhauser, pp. 157-172.
  5. DeCarli, D J. 1970. A generalized Fibonacci sequence over an arbitrary’ ring. The
    Fibonacci Quarterly. 8.2: 182-184.
  6. Dilcher, Karl. 1998. Nested squares and evaluations of integer products. 8th International Conference on Fibonacci Numbers and Their Applications, Rochester, USA, 22-26 June.
  7. Hoggatt, V E. Jr. 1969. Fibonacci and Lucas Numbers. Boston: Houghton Mifflin.
  8. Horadam, A. F. 1965. Generating functions for powers of a certain generalized sequence of numbers. Duke Mathematical Journal. 32.3: 437-446.
  9. Leyendekkers, J V, Rybak, J M & Shannon, A G. 1997. Analysis of Diophantine properties using modular rings with four and six classes. Notes on Number Theory & Discrete Mathematics. 3.2: 61-74.
  10. Leyendekkers, J V, Rybak, J M & Shannon, A G. 1998. The characteristics of primes and other integers within the modular ring Z4 and in class 1. Notes on Number Theory & Discrete Mathematics. 4.1: 1-17.
  11. Morgan, Mark D. 1998. The distribution of second order linear recurrence sequences mod 2m. Acta Arithmetica. 83.2: 181-195.
  12. Shannon, A.G. 1972. Iterative formulas associated with third order recurrence relations.
    S.I.A.M. Journal of Applied Mathematics. 23.3: 364-368.
  13. Shannon, A.G. 1974. Some properties of a fundamental linear recursive sequence of arbitrary order. The Fibonacci Quarterly. 12.4: 327-335.
  14. Stein, S.K. 1962. The intersection of Fibonacci sequences. The Michigan Mathematics Journal. 9: 399-402.
  15. Wyler, O. 1965. On second order recurrences. American Mathematical Monthly. 72.5: 500-506.

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Cite this paper

Leyendekkers, J. V. & Shannon, A. G. (1998). Title. Notes on Number Theory and Discrete Mathematics, 4(4), 165-174.

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