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Matematicheskie Zametki, 2010, Volume 88, Issue 4, Pages 594–604
DOI: https://doi.org/10.4213/mzm8854 (Mi mzm8854) 		 
This article is cited in 8 scientific papers (total in 8 papers)

The Mean Number of Steps in the Euclidean Algorithm with Odd Incomplete Quotients

A. V. Ustinov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
Full-text PDF (494 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm8854
Abstract: The length of the continued-fraction expansion of a rational number with odd incomplete quotients is expressed via the Gauss–Kuzmin statistics for the classical continued fraction. This has made it possible to prove asymptotic formulas, similar to those already known for the classical Euclidean algorithm, for the mean length of the Euclidean algorithm with odd incomplete quotients.
Keywords: Euclidean algorithm, Gauss–Kuzmin statistics, continued-fraction expansion, dual fraction, incomplete quotient.
Received: 13.04.2010
English version:
Mathematical Notes, 2010, Volume 88, Issue 4, Pages 574–584
DOI: https://doi.org/10.1134/S0001434610090300
Bibliographic databases:
Document Type: Article
UDC: 517.524+510.52+519.712.61
Language: Russian
Citation: A. V. Ustinov, “The Mean Number of Steps in the Euclidean Algorithm with Odd Incomplete Quotients”, Mat. Zametki, 88:4 (2010), 594–604; Math. Notes, 88:4 (2010), 574–584
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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