The mean number of steps in the Euclidean algorithm with odd partial quotients

Author: Ustinov A.  

Publisher: MAIK Nauka/Interperiodica

ISSN: 0001-4346

Source: Academy of Sciences of the USSR Mathematical Notes, Vol.88, Iss.3-4, 2010-10, pp. : 574-584

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Abstract

The length of the continued-fraction expansion of a rational number with odd partial quotients is expressed via the Gauss-Kuz'min 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 partial quotients.