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Mat. Zametki, 2008, Volume 84, Issue 2, Pages 281–299 (Mi mz4074)  

A Special Matrix Transformation Semigroup of Primitive Pairs and the Genealogy of Pythagorean Triples

V. E. Firstov

Saratov State University named after N. G. Chernyshevsky

Abstract: 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, Diophantine equation, Pythagorean triple, genealogy of Pythagorean triples, semigroup, complete countable graph

DOI: https://doi.org/10.4213/mzm4074

Full text: PDF file (679 kB)
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English version:
Mathematical Notes, 2008, 84:2, 263–279

Bibliographic databases:

UDC: 512.534.7+519.17
Received: 16.05.2007
Revised: 19.10.2007

Citation: V. E. Firstov, “A Special Matrix Transformation Semigroup of Primitive Pairs and the Genealogy of Pythagorean Triples”, Mat. Zametki, 84:2 (2008), 281–299; Math. Notes, 84:2 (2008), 263–279

Citation in format AMSBIB
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