The anatomy of odd-exponent Diophantine triples

J. V. Leyendekkers, J. M. Rybak and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 3, 1997, Number 1, Pages 41–51
Full paper (PDF, 291 Kb)

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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

In similar manner to the analysis for even-exponent triples, this paper uses the equivalence classes of the modular ring ℤ₆ to show why the diophantine equation d^m = e^m + f^m, where m is odd, is limited to m = 1 in ℤ₆.

References

1.  J.V. Leyendekkers, J.M. Rybak and A.G. Shannon, The anatomy of even exponent Pythagorean triples. Notes on Number Theory and Discrete Mathematics, 2, 1, 1996, 33-52.
2.  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.
3.  Alf van der Poorten, Notes on Fermat’s Last Theorem; New York: Wiley, 1996.