Jathan Austin
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 2, Pages 402–406
DOI: 10.7546/nntdm.2023.29.2.402-406
Full paper (PDF, 145 Kb)
Details
Authors and affiliations
Jathan Austin 
Department of Mathematical Sciences, Salisbury University
Salisbury, Maryland, United States
Abstract
We present matrices that generate families of primitive Pythagorean triples that arise from generalized Fibonacci sequences. We then present similar results for generalized Lucas sequences and primitive Pythagorean triples.
Keywords
- Pythagorean triples
- Fibonacci and Lucas numbers
2020 Mathematics Subject Classification
- 11B39
- 11C20
References
- Austin, J., & Schneider, L. (2020). Generalized Fibonacci numbers in Pythagorean triple preserving matrices. The Fibonacci Quarterly, 58(4), 340–350.
- Burton, D. M. (2010). Elementary Number Theory. New York: McGraw Hill.
- Leyendekkers, J. V., & Shannon, A. G. (2016). Primitive Pythagorean triples and generalized Fibonacci sequences. Notes on Number Theory and Discrete Mathematics, 23(1), 54–62.
- Palmer, L., Ahuja, M., & Tikoo, M. (1998). Finding Pythagorean triple preserving matrices. Missouri Journal of Mathematical Sciences, 10(2), 99–105
Manuscript history
- Received: 19 March 2023
- Accepted: 22 May 2023
- Online First: 27 May 2023
Copyright information
Ⓒ 2023 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Related papers
- Leyendekkers, J. V., & Shannon, A. G. (2016). Primitive Pythagorean triples and generalized Fibonacci sequences. Notes on Number Theory and Discrete Mathematics, 23(1), 54–62.
Cite this paper
Austin, J. (2023). A note on generating primitive Pythagorean triples using matrices. Notes on Number Theory and Discrete Mathematics, 29(2), 402-406, DOI: 10.7546/nntdm.2023.29.2.402-406.
