Recurrence relation analysis of Pythagorean triple patterns

J. M. Rybak, J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132
Volume 1, 1995, Number 1, Pages 1–10
Full paper (PDF, 5.5 Mb

Details

Authors and affiliations

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

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

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

Abstract

This paper explores recurrence relations in their role of providing internal generators of Pythagorean triples. While the relation of Pellian recurrence relations to Diophantine equations in general is not new, this paper classifies the internal generators according to their parity and primality.

AMS Classification

• 11D09
• 11B37

References

1. J. V. Leyendekkers and J. Rybak, The generation and analysis of Pythagorean triples within a two-parameter grid. International Journal of Mathematical Education in Science and Technology у in press.
2. J. V. Leyendekkers and J. Rybak, Pellian sequences derived from Pythagorean triples. International Journal of Mathematical Education in Science and Technology, in press.
3. A. F. Horadam and A. G. Shannon, Pell-type number generators of Pythagorean triples, in G. E. Bergum et al (eds.), Applications of Fibonacci Numbers, Vol. 5, Kluwer, Dordrecht, 1993, 331-343.
4. A. G. Shannon and A. F. Horadam, Arrowhead curves in a tree of Pythagorean triples, International Journal of Mathematical Education in Science and Technology, 25.2 (1994): 225-261.