The Farey Sum of Pythagorean and Eisenstein Triples

Authors : Mircea Crasmareanu

Pages : 28-35

Doi:10.36753/mathenot.1316554

View : 189 | Download : 56

Publication Date : 2024-01-28

Article Type : Research Paper

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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