Integer structure and constraints on powers within the modular ring ℤ4 – Part II: Odd powers

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
Download full paper: PDF, 3398 Kb

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 ℤ4. As for even powers, all pathways to an integer solution for cnan = bn, n > 2, are essentially blocked by the class structure and row nesting characteristics as well as the parity requirements.

AMS Classification

  • 11C08
  • 11D41

References

  1. Hillman, Abraham P & Gerald L Alexanderson. 1973. A First Undergraduate Course in Abstract Algebra. Belmont, CA: Wadsworth.
  2. Hunter, J. 1964. Number Theory. Edinburgh: Oliver and Boyd.
  3. 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.
  4. 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.
  5. Leyendekkers, J. V. & A. G. Shannon. 2001. Integer Structure and Constraints on Powers within the Modular Ring ℤ4 – Part I: Even Powers. Notes on Number Theory & Discrete Mathematics. Submitted.
  6. McCoy, N.H. 1948. Rings and Ideals. Washington, DC: Mathematical Association of America.
  7. van der Poorten, A. 1996. Notes on Fermafs Last Theorem. New York: Wiley.

Related papers

Cite this paper

APA

Leyendekkers, J., & Shannon, A. (2002). Integer structure and constraints on powers within the modular ring ℤ4 – Part II: Odd powers. Notes on Number Theory and Discrete Mathematics, 8(2), 58-66.

Chicago

Leyendekkers, JV, and AG Shannon. “Integer Structure and Constraints on Powers within the Modular Ring ℤ4 – Part II: Odd Powers.” Notes on Number Theory and Discrete Mathematics 8, no. 2 (2002): 58-66.

MLA

Leyendekkers, JV, and AG Shannon. “Integer Structure and Constraints on Powers within the Modular Ring ℤ4 – Part II: Odd Powers.” Notes on Number Theory and Discrete Mathematics 8.2 (2002): 58-66. Print.

Comments are closed.