# Continued Fractions

```@inproceedings{Lasjaunias1999ContinuedF,
title={Continued Fractions},
author={Alain Lasjaunias},
year={1999}
}```
The study of continued fractions is an ancient part of elementary Number Theory. It was studied by Leonhard Euler in the 18-th century. Actually, a remarkable paper from him was translated from Latin language into English and published thirty years ago [1]. The subject has been treated very deeply by Oskar Perron at the beginning of the 20 th century, in a famous book which has been edited several times [2]. It can also be found in several books on Number Theory, among them a famous one is “An…
1,465 Citations
On the periodicity of an algorithm for p-adic continued fractions
• Mathematics
• 2022
In this paper we study the properties of an algorithm (introduced in [6]) for generating continued fractions in the field of p–adic numbers Qp. First of all, we obtain an analogue of the Galois’
On Continued Fractions
This paper on the geometry, algebra and arithmetics of continued fractions is based on a lecture for students, teachers and a non-specialist audience, beginning with the history of the golden number
Intermediate convergents and a metric theorem of Khinchin
A landmark theorem in the metric theory of continued fractions begins this way: Select a non‐negative real function f defined on the positive integers and a real number x, and form the partial sums
Prime Numbers and the Convergents of a Continued Fraction
Continued fractions offer a concrete representation for arbitrary real numbers. The continued fraction expansion of a real number is an alternative to the representation of such a number as a
Orderings of the rationals and dynamical systems
• Mathematics, Computer Science
• 2008
A class of one-dimensional maps is introduced which can be used to generate the binary trees in dierent ways and study their ergodic properties and some random processes arising in a natural way in this context.
Continued fractions in non-Euclidean imaginary quadratic fields.
In the Euclidean imaginary quadratic fields, continued fractions have been used to give rational approximations to complex numbers since the late 19th century. A variety of algorithms have been
On Consecutive 1’s in Continued Fractions Expansions of Square Roots of Prime Numbers
• Mathematics
Experimental Mathematics
• 2019
Abstract In this note, we study the problem of existence of sequences of consecutive 1’s in the periodic part of the continued fractions expansions of square roots of primes. We prove unconditionally

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