Analysis of odd exponent triples within the modular ring ℤ₄ using binomial expansions and Fermat reductions

J. V. Leyendekkers, J. M. Rybak and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 3, 1997, Number 3, Pages 128–158
Full paper (PDF, 967 Kb)

Details

Authors and affiliations

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

J. M. Rybak
The University of Sydney, 2006, Australia

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

Abstract

The essential characteristics of integers and the relationships with their powers are explored within the framework of the modular ring ℤ₄ in order to analyze why odd powered triples with exponents greater than unity cannot exist in integer form. Two methods are given which exploit old expansion and reduction techniques in a new way. By way of conclusion the second method is also illustrated by reference to Pythagorean triples.

AMS Classification

• 11D41
• 11D99

References

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