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
Download 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.