A. P. Chaves

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math.NT2025

Diophantine equations over the generalized Fibonacci sequences: exploring sums of powers

Roberto Alvarenga, Ana Paula Chaves, Maria Eduarda Ramos +2

Let (F_n)_{n} be the classical Fibonacci sequence. It is well-known that it satisfies F_{n}^2 + F_{n+1}^2 = F_{2n+1}. In this study, we explore generalizations of this Diophantine…

math.NT2025

Fibonacci Numbers as Sums of Consecutive Terms in $k$ -Generalized Fibonacci Sequence

Roberto Alvarenga, Ana Paula Chaves, Maria Eduarda Ramos +2

Let (F_n^{(k)})_{n\geq -(k-2)} be the k-generalized Fibonacci sequence, defined as the linear recurrence sequence whose first k terms are $0, 0, \ldots, 0, 1$, and whose subseque…

math.NT2019

On the Arithmetic Behavior of Liouville Numbers under Rational Maps

Ana Paula Chaves, Diego Marques, Pavel Trojovsk\' y

In 1972, Alniaçik proved that every strong Liouville number is mapped into the set of $U_{m}$ -numbers, for any non-constant rational function with coefficients belonging to an $m$ -de…

math.NT2019

Double-Recurrence Fibonacci Numbers and Generalizations

Carlos Alirio Rico Acevedo, Ana Paula Chaves

Let $(F_{n})_{n \geq 0}$ be the Fibonacci sequence given by the recurrence $F_{n + 2} = F_{n + 1} + F_{n}$ , for $n \geq 0$ , where $F_{0} = 0$ and $F_{1} = 1$ . There are several generalizations of this s…

math.NT2009

Transcendence Measures for some $U_{m}$ -numbers related to Liouville's constant

Ana Paula Chaves, Diego Marques

In this note, we shall prove that the sum and the product of an algebraic number $α$ by the \textit{Liouville constant} $L = \sum_{j = 1}^{\infty} 1 0^{- j!}$ is a $U$ -number with type eq…