J. V. Leyendekkers, A. G. Shannon and C. K. Wong

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 15, 2009, Number 4, Pages 13—22

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## Details

### 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
*

C. K. Wong

*Warrane College, The University of New South Wales
Kensington, NSW 1465, Australia
*

### Abstract

Certain characteristics of Pythagorean triples are analysed using Integer Structure via the modular ring, *Z*_{4}. The fact (as shown by Fermat’s Last Theorem) that all the components of a triple cannot simultaneously be an even power *n* (with ½*n* even) is illustrated via the spectra of the right-end-digits of the components.

### Keywords

- Pythagorean triples
- Right end digits
- Integer structure analysis
- Modular rings

### AMS Classification

- 11D41
- 11A07

### References

- Aczel, Amir D. 1997. Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem. New York: Delta.
- Artin, Emil. Otto Schreier. Algebraische Konstruktion reeler Körper. Abhandlungen aus dem Mathematichen Seminar der Universität Hamburg. 5, 1927:85-99.
- Leyendekkers, J.V., A.G. Shannon, J.M. Rybak. Pattern Recognition: Modular Rings and Integer Structure. North Sydney: Raffles KvB Monograph No.9, 2007.
- Zassenchaus, H., Emil Artin. His Life and Work. Notre Dame Journal of Formal Logic. 5, 1964: 1-9.

## Related papers

## Cite this paper

APALeyendekkers, J. V., Shannon, A. G., & Wong, C. K. (2009). Structure and spectra of the components of primitive Pythagorean triples and Fermat’s last theorem. Notes on Number Theory and Discrete Mathematics, 15(4), 13-22.

ChicagoLeyendekkers, JV, AG Shannon and CK Wong. “Structure and Spectra of the Components of Primitive Pythagorean Triples and Fermat’s Last Theorem.” Notes on Number Theory and Discrete Mathematics 15, no. 4 (2009): 13-22.

MLALeyendekkers, JV, AG Shannon and CK Wong. “Structure and Spectra of the Components of Primitive Pythagorean Triples and Fermat’s Last Theorem.” Notes on Number Theory and Discrete Mathematics 15.4 (2009): 13-22. Print.