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Matematicheskie Zametki, 2008, Volume 84, Issue 2, Pages 281–299
DOI: https://doi.org/10.4213/mzm4074 (Mi mzm4074) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (679 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm4074
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.
Received: 16.05.2007
Revised: 19.10.2007
English version:
Mathematical Notes, 2008, Volume 84, Issue 2, Pages 263–279
DOI: https://doi.org/10.1134/S0001434608070262
Bibliographic databases:
UDC: 512.534.7+519.17
Language: Russian
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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  • https://www.mathnet.ru/eng/mzm/v84/i2/p281
    • This publication is cited in the following 2 articles:
    1. Howard Sporn, “Forringer's Method and More Trees of Pythagorean Triples”, The College Mathematics Journal, 54:4 (2023), 269  crossref
    2. Victor Egorovitch Firstov, “Semantic model and optimization of creative processes at mathematical knowledge formation”, NS, 02:08 (2010), 915  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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