Continued fractions have a long history in number theory, especially in the area of
Diophantine approximation. The aim of this expository paper is to survey the main results on …

Continued fractions have been widely studied in the field of $ p $-adic numbers $\mathbb
Q_p $, but currently there is no algorithm replicating all the good properties that continued …

Continued fractions have a long history in number theory, especially in the area of
Diophantine approximation. The aim of this expository paper is to survey the main results on …

Continued fractions can be introduced in the field of p-adic numbers Q p, however currently
there is not a standard algorithm as in R. Indeed, it is not known how to construct p-adic …

In this paper, we provide a periodic representation (by means of periodic rational or integer
sequences) for any cubic irrationality. In particular, for a root α of a cubic polynomial with …

In this paper we present some results related to the problem of finding periodic
representations for algebraic numbers. In particular, we analyze the problem for cubic …

Let $ p $ be a prime number and $ K $ be a field with embeddings into $\mathbb {R} $ and
$\mathbb {Q} _p $. We propose an algorithm that generates continued fraction expansions …

In this paper, the Hermite problem has been approached finding a periodic representation
(by means of periodic rational or integer sequences) for any cubic irrationality. In other …

The paper is devoted to the problem of representing and approximating quadratic
irrationalities. In particular, a new manageable periodic representation of period 2 and pre …

The Problem of approximation of an irrational number 'θ'has been discussed on this paper,
by confining the study upto approximation of quadratic irrationals only. Three theorems have …