Integer structure and constraints on powers within the modular ring ℤ₄ – Part I: Even powers

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 8, 2002, Number 2, Pages 41–57
Full paper (PDF, 7877 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 constraints, which prevent sums or differences of identical powers, n, from equalling a power of the same value (n > 2), are explored within the Modular Ring, ℤ₄. Although the integer structure is complex, the results agree with those obtained for the octic or chess ring, which showed that the specific class structure, row nesting and other characteristics for powers give rise to a row exclusion factor in the modular tables of residues. This factor ensures that the resultant value of two coupled identical powers can never fit into a slot within ℤ₄ which is reserved for a power of the same value.

AMS Classification

• 11C08
• 11D41

References

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