Geodesic
A Special Matrix Transformation Semigroup of Primitive Pairs and the Genealogy of Pythagorean Triples
Matematičeskie zametki, Tome 84 (2008) no. 2, pp. 281-299.

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A special matrix semigroup acting on the set of primitive pairs of positive integers naturally parameterizing certain Diophantine equations (such as those defining Pythagorean triples) is constructed and studied. The Pythagorean triples are related to a trichotomy tree of solutions.
Keywords: Pythagorean problem, Pythagorean triple, genealogy of Pythagorean triples, semigroup, complete countable graph.
Mots-clés : Diophantine equation 
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V. E. Firstov. A Special Matrix Transformation Semigroup of Primitive Pairs and the Genealogy of Pythagorean Triples. Matematičeskie zametki, Tome 84 (2008) no. 2, pp. 281-299. http://geodesic.mathdoc.fr/item/MZM_2008_84_2_a9/

[1] V. E. Firstov, Netraditsionnye geometricheskie interpretatsii, polugruppovaya teoriya i genealogiya pifagorovykh troek, Izd-vo “Nauchnaya kniga”, Saratov, 2004

[2] A. Hall, “Genealogy of pythagorean triads”, Math. Gaz., 54 (1970), 377–379 | DOI

[3] E. S. Selmer, “Organisering av Pytagoreiske tallsett”, Nordisk Mat. Tidskr., 25–26:3–4 (1978), 139–149 | MR | Zbl