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


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


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Cite this paper

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

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