The Farey Sum of Pythagorean and Eisenstein Triples

Year 2024, Volume: 12 Issue: 1, 28 - 35, 28.01.2024

Mircea Crasmareanu

https://doi.org/10.36753/mathenot.1316554

Abstract

A composition law, inspired by the Farey addition, is introduced on the set of Pythagorean triples. We study some of its properties as well as two symmetric matrices naturally associated to a given Pythagorean triple. Several examples are discussed, some of them involving the degenerated Pythagorean triple $(1, 0, 1)$. The case of Eisenstein triples is also presented.

Keywords

Farey sum, Pythagorean (Eisenstein) triple, Symmetric matrix

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