Metallic means and Pythagorean triples

Chetansing Rajput and Hariprasad Manjunath
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 1, Pages 184–194
DOI: 10.7546/nntdm.2024.30.1.184-194
Full paper (PDF, 359 Kb)

Details

Authors and affiliations

Chetansing Rajput
Asst. Commissioner, Government of Maharashtra
Mumbai, India

Hariprasad Manjunath
INRIA Center Université Côte d’Azur, France

Abstract

In this article, we study the connection between Pythagorean triples and metallic means. We derive several interconnecting identities between different metallic means. We study the Pythagorean triples in the three-term recurrent sequences corresponding to different metallic means. Further, we relate different families of primitive Pythagorean triples to the corresponding metallic means.

Keywords

• Fibonacci sequence
• Golden ratio
• Primitive Pythagorean triples
• Metallic means

2020 Mathematics Subject Classification

• 11A05
• 11-01

References

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Manuscript history

• Received: 11 August 2023
• Revised: 28 January 2024
• Accepted: 21 March 2024
• Online First: 25 March 2024

Copyright information

Ⓒ 2024 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).