Volume no :10, Issue no: 1-2, September and December (2013)

Journal of Algebra, Number Theory: Advances and Applications

A NOTE ON CERTAIN RELATIONS BETWEEN THE FIBONACCI SEQUENCE AND THE EUCLIDEAN ALGORITHM

Author's: NAOTO ONDA
Pages: [29] - [39]
Received Date: December 31, 2013; Revised January 8, 2014
Submitted by:

Abstract

Gabriel Lame gave an upper bound of the number of steps in the Euclidean algorithm. In this paper, we show that for the integer belonging to “Lucas set” and a positive integer less than the maximum number of steps in the Euclidean algorithm is equal to

Keywords

Euclidean algorithm, Fibonacci sequence.