The modular ring ℤ6 and the area of a Pythagorean triangle

J. V. Leyendekkers, J. M. Rybak and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 3, 1997, Number 3, Pages 173—175
Download full paper: PDF, 89 Kb

Details

Authors and affiliations

J. V. Leyendekkers
The University of Sydney, 2006, Australia

J. M. Rybak
The University of Sydney, 2006, Australia

A. G. Shannon
University of Technology, Sydney, 2007, Australia

Abstract

Fermat used the method of infinite descent to show that the area of a Pythagorean triangle can never be a square. Here we use the modular ring ℤ6 [1] to obtain the same result.

References

  1. J.V. Leyendekkers, J.M. Rybak and A.G. Shannon, Integer Class Properties Associated with an integer Matrix. Notes on Number Theory and Discrete Mathematics, 1, 2, 1995, 53-59.
  2. J.V. Leyendekkers and J.M. Rybak, The generation and analysis of Pythagorean triples within a two-parameter grid. International Journal of Mathematical Education in Science and Technology 26, 6, 1995, 787-793.

Related papers

Cite this paper

APA

Leyendekkers, J. V., Rybak, J. M. & Shannon, A. G. (1997). The modular ring ℤ6 and the area of a Pythagorean triangle. Notes on Number Theory and Discrete Mathematics, 3(3), 173-175.

Chicago

Leyendekkers, J. V., Rybak, J. M. & Shannon, A. G. “The modular ring ℤ6 and the area of a Pythagorean triangle.” Notes on Number Theory and Discrete Mathematics 3, no. 3 (1997): 173-175.

MLA

Leyendekkers, J. V., Rybak, J. M. & Shannon, A. G. “The modular ring ℤ6 and the area of a Pythagorean triangle.” Notes on Number Theory and Discrete Mathematics 3.3 (1997): 173-175. Print.

Comments are closed.