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March 27, 2026Open Access

Metallic Means and Pythagorean Triples

Key Points

The aim is to explore the relationship between Pythagorean triples and metallic means, revealing interconnected identities.
Derived identities involving different metallic means
Examined Pythagorean triples in three-term recurrent sequences
Related primitive Pythagorean triples to corresponding metallic means
Identified several interconnecting identities between metallic means
Established relationships with three-term recurrent sequences
Connected families of primitive Pythagorean triples to metallic means

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. © 2024 by the Authors. 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). https://creativecommons.org/licenses/by/4.0/

Metallic Means and Pythagorean Triples

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Abstract

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