The integer structure of the difference of two odd integers raised to an even power

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 16, 2010, Number 1, Pages 1–4
Full paper (PDF, 148 Kb)

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Authors and affiliations

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

A. G. Shannon
Warrane College, The University of New South Wales
Kensington, NSW 1465, Australia

Abstract

Using the modular ring Z4, it is shown that the row structures of xn − yn, x, y odd, n = 2m, are incompatible with the row structures of zn. Even though some structures are close, the right-end-digits (REDs) are quite distinct. The analysis shows how the effort to find counter-examples for such theorems may be drastically reduced.

Keywords

  • Primes
  • Composites
  • Modular rings
  • Right-end digits
  • Integer structure

AMS Classification

  • 11A41
  • 11A07

References

  1. Leyendekkers, J.V., A.G. Shannon. 2006. Integer Structure Analysis of Primes and Composites from Sums of Two Fourth Powers. Notes on Number Theory & Discrete Mathematics. 12(3): 1-9.
  2. Leyendekkers, J.V., A.G. Shannon. 2007. Modular Ring Class Structures of xn ± yn. Notes on Number Theory & Discrete Mathematics. 13(3): 27-35.
  3. Leyendekkers, J.V., A.G. Shannon. 2009. The Integer Structure of the Difference of Two Odd-Powered Odd Integers. Notes on Number Theory & Discrete Mathematics. 15(3): 14-20.

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Cite this paper

Leyendekkers, J. V., and Shannon, A. G. (2010). The integer structure of the difference of two odd integers raised to an even power. Notes on Number Theory and Discrete Mathematics, 16(1), 1-4.

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