Powers as a difference of squares: The effect on triples

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 8, 2002, Number 3, Pages 95—106
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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

All powers equal a difference of squares so that triples may be expressed as the sum of three squares which equal the sum of another three squares. However, when n > 2 integer values for all the components should be impossible according to the work which peaked with Wiles. By utilizing the properties of the Modular Ring ℤ4 we illustrate how the underlying Class structures of the integers justifies this constraint.

AMS Classification

  • 11C08
  • 11D41

References

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  4. Leyendekkers, J.V., Rybak, J.M. & Shannon, A.G. 1997. Analysis of Diophantine Properties Using Modular Rings with Four and Six Classes. Notes on Number Theory & Discrete Mathematics. Vol.3(2): 61-74.
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  6. Leyendekkers, J.V. & Shannon, A.G. 2001. Expansion of Integer Powers from Fibonacci’s Odd Number Triangle. Notes on Number Theory & Discrete Mathematics. Vol.7(2): 48-59.
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Cite this paper

APA

Leyendekkers, J., & Shannon, A. (2002). Powers as a difference of squares: The effect on triples. Notes on Number Theory and Discrete Mathematics, 8(3), 95-106.

Chicago

Leyendekkers, J., & Shannon, A. “Powers as a difference of squares: The effect on triples.” Notes on Number Theory and Discrete Mathematics 8, no. 3 (2002): 95-106.

MLA

Leyendekkers, J., & Shannon, A. “Powers as a difference of squares: The effect on triples.” Notes on Number Theory and Discrete Mathematics 8.3 (2002): 95-106. Print.

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