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
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 cn − an = bn, n > 2, are essentially blocked by the class structure and row nesting characteristics as well as the parity requirements.
- 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 ℤ4 – 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.
- 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.
Cite this paper
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.