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
Full paper (PDF, 1495 Kb)

Details

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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