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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## 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

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 ℤ_{4} we illustrate how the underlying Class structures of the integers justifies this constraint.

### AMS Classification

- 11C08
- 11D41

### References

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Hunter, J. 1964. Number Theory. Edinburgh: Oliver and Boyd. - 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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## Cite this paper

APALeyendekkers, 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.

ChicagoLeyendekkers, 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.

MLALeyendekkers, 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.