J. V. Leyendekkers and A. G. Shannon

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

Volume 8, 2002, Number 2, Pages 58—66

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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

The integer structure of triples with an odd exponent is explored within the Modular Ring ℤ_{4}. As for even powers, all pathways to an integer solution for *c ^{n}* −

*a*=

^{n}*b*,

^{n}*n*> 2, are essentially blocked by the class structure and row nesting characteristics as well as the parity requirements.

### AMS Classification

- 11C08
- 11D41

### References

- Hillman, Abraham P & Gerald L Alexanderson. 1973. A First Undergraduate Course in Abstract Algebra. Belmont, CA: Wadsworth.
- Hunter, J. 1964. Number Theory. Edinburgh: Oliver and Boyd.
- Knapowski, S. & Turan, P. 1977. On Prime Numbers = 1 resp. 3 mod 4. In Hans Zassenhaus (ed.), Number Theory and Algebra. New York: Academic Press, pp. 157-165.
- Leyendekkers, J.V., Rybak, J.M. & A. G. Shannon. 1997. Analysis of Diophantine Properties Using Modular Rings with Four and Six Classes. Notes on Number Theory & Discrete Mathematics. 3(2): 61-74.
- Leyendekkers, J. V. & A. G. Shannon. 2001. Integer Structure and Constraints on Powers within the Modular Ring ℤ
_{4}– Part I: Even Powers. Notes on Number Theory & Discrete Mathematics. Submitted. - McCoy, N.H. 1948. Rings and Ideals. Washington, DC: Mathematical Association of America.
- van der Poorten, A. 1996. Notes on Fermafs Last Theorem. New York: Wiley.

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## Cite this paper

APALeyendekkers, J., & Shannon, A. (2002). Integer structure and constraints on powers within the modular ring ℤ_{4} – Part II: Odd powers. Notes on Number Theory and Discrete Mathematics, 8(2), 58-66.

Leyendekkers, JV, and AG Shannon. “Integer Structure and Constraints on Powers within the Modular Ring ℤ_{4} – Part II: Odd Powers.” Notes on Number Theory and Discrete Mathematics 8, no. 2 (2002): 58-66.

Leyendekkers, JV, and AG Shannon. “Integer Structure and Constraints on Powers within the Modular Ring ℤ_{4} – Part II: Odd Powers.” Notes on Number Theory and Discrete Mathematics 8.2 (2002): 58-66. Print.