Integer structure and constraints on powers within the modular ring ℤ₄ – Part II: Odd powers

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 8, 2002, Number 2, Pages 58–66
Full paper (PDF, 3398 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

The integer structure of triples with an odd exponent is explored within the Modular Ring ℤ₄. As for even powers, all pathways to an integer solution for cⁿ − aⁿ = bⁿ, n > 2, are essentially blocked by the class structure and row nesting characteristics as well as the parity requirements.

AMS Classification

• 11C08
• 11D41

References

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