Lehmer's GCD algorithm

Mirjam Kolar (2015) Lehmer's GCD algorithm. EngD thesis.

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Abstract

In this thesis we briefly look at the rules related to the greatest common divisor and the lowest common multiple of two integers and we describe the Euclidean algorithm. We study connections between Euclidean algorithm and continued fractions, Wirsing's method for determining the distribution function and how Knuth calculated the distribution of partial quotients in Euclidean algorithm using this method. Next Lehmer's algorithm is described and how it improves Euclidean algorithm, greatest common divisor and the multiplicative inverse mod n for a natural number n. We implement both Euclidean algorithm and Lehmer's algorithm in order to compare their speed. We also confirm the calculated distributions of partial quotients in Euclidean algorithm through an experiment.

Item Type:

Thesis (EngD thesis)

Keywords:

Lehmer's algorithm, Euclidean algorithm, continued fractions, distribution function, Wirsing's method for determining the distribution function, quotients in Euclidean algorithm.

Number of Pages:

Language of Content:

Slovenian

Mentor / Comentors:

Name and Surname	ID	Function
prof. dr. Aleksandar Jurišić	1118	Mentor
prof. dr. Roman Drnovšek	3483	Comentor

Link to COBISS:

http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1536211651)

Institution:

University of Ljubljana

Department:

Faculty of Computer and Information Science

Item ID:

2905

Date Deposited:

23 Jan 2015 15:26

Last Modified:

03 Mar 2015 12:47

URI:

http://eprints.fri.uni-lj.si/id/eprint/2905

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