Expansion of integer powers from Fibonacci’s odd number triangle

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 7, 2001, Number 2, Pages 48—59
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Authors and affiliations

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

A. G. Shannon
Warrane College, The University of New South Wales, 1465, &
KvB Institute of Technology, North Sydney, 2060, Australia

Abstract

Cubes and squares are expanded in various ways stimulated by Fibonacci’s odd number triangle which is in turn extended to even powers. The class structure of the cubes within the modular ring ℤ4 is developed. This provides constraints for the various functions which help in solving polynomial and Diophantine equations, some simple examples of which are given.

AMS Classification

  • 11C08
  • 11B39

References

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  6. Leyendekkers, JV, Rybak, 1M & Shannon, AG. 1997. Analysis of Diophantine Properties Using Modular Rings with Four and Six Classes. Notes on Number Theory & Discrete Mathematics. VoI. 3(2): 61-74.
  7. Mason, John. 2001. Generalising ‘Sums of Cubes Equal to Squares of Sums’. Mathematical Gazette. Vol. 85(502): 50-58.
  8. Müller, Siguna. 2000. Some Remarks on Primality Testing Based on Lucas Sequences. Ninth International Conference on Fibonacci Numbers and Their Applications, Luxembourg, 17-22 July.
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Cite this paper

APA

Leyendekkers, J., & Shannon, A. (2001). The decimal string of the golden ratio. Notes on Number Theory and Discrete Mathematics, 7(2), 48-59.

Chicago

Leyendekkers, JV, and AG Shannon. “The Decimal String of the Golden Ratio.” Notes on Number Theory and Discrete Mathematics 7, no. 2 (2001): 48-59.

MLA

Leyendekkers, JV, and AG Shannon. “The Decimal String of the Golden Ratio.” Notes on Number Theory and Discrete Mathematics 7.2 (2001): 48-59. Print.

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