Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On the problem of Pillai with Pell numbers, Pell–Lucas numbers and powers of 3
View through CrossRef
Let [Formula: see text] be the sequence of Pell numbers defined by [Formula: see text], [Formula: see text] and [Formula: see text] for all [Formula: see text] and let [Formula: see text] be its companion sequence, the Pell–Lucas numbers defined by [Formula: see text] and [Formula: see text] for all [Formula: see text]. In this paper, we find all integers [Formula: see text] admitting at least two representations as a difference between a Pell number or a Pell–Lucas number and a power of [Formula: see text]
World Scientific Pub Co Pte Ltd
Title: On the problem of Pillai with Pell numbers, Pell–Lucas numbers and powers of 3
Description:
Let [Formula: see text] be the sequence of Pell numbers defined by [Formula: see text], [Formula: see text] and [Formula: see text] for all [Formula: see text] and let [Formula: see text] be its companion sequence, the Pell–Lucas numbers defined by [Formula: see text] and [Formula: see text] for all [Formula: see text].
In this paper, we find all integers [Formula: see text] admitting at least two representations as a difference between a Pell number or a Pell–Lucas number and a power of [Formula: see text].
Related Results
On Hybrid Hyper k-Pell, k-Pell–Lucas, and Modified k-Pell Numbers
On Hybrid Hyper k-Pell, k-Pell–Lucas, and Modified k-Pell Numbers
Many different number systems have been the topic of research. One of the recently studied number systems is that of hybrid numbers, which are generalizations of other number syste...
Some Binomial Sums of k-Pell, k-Pell-Lucas and Modified k-Pell Numbers
Some Binomial Sums of k-Pell, k-Pell-Lucas and Modified k-Pell Numbers
The main goal of this paper is to find some new identities containing k-Pell and k-Pell-Lucas numbers. In addition, we use these identities to prove binomial properties of k-Pell, ...
On generalized (k, r)-Pell and (k, r)-Pell–Lucas numbers
On generalized (k, r)-Pell and (k, r)-Pell–Lucas numbers
We introduce new kinds of k-Pell and k-Pell–Lucas numbers related to the distance between numbers by a recurrence relation and show their relation to the (k,r)-Pell and (k,r)-Pell–...
The Properties of the Altered Pell and Pell Lucas Sequences
The Properties of the Altered Pell and Pell Lucas Sequences
The altered Pell and Pell Lucas sequences are defined by altering the Pell and Pell Lucas numbers, it is seen that they have similar properties to usual the Pell and Pell Lucas seq...
Automaquiagem com Lucas Vieira Funciona? | Automaquiagem com Lucas Vieira Site Oficial | Automaquiagem com Lucas Vieira é Confiável?
Automaquiagem com Lucas Vieira Funciona? | Automaquiagem com Lucas Vieira Site Oficial | Automaquiagem com Lucas Vieira é Confiável?
Automaquiagem com Lucas Vieira Funciona? | Automaquiagem com Lucas Vieira Site Oficial | Automaquiagem com Lucas Vieira é Confiável?
Automaquiagem com Lucas Vieira: Tudo o Que Vo...
Gaussian (????, ????)-Pell and Pell-Lucas Sequences and Their Matrix Representations
Gaussian (????, ????)-Pell and Pell-Lucas Sequences and Their Matrix Representations
In this study, we define the Gaussian (s,t)-Pell and Gaussian (s,t)-Pell-Lucas sequences. Then, by using
these sequences we define Gaussian (s,t)-Pell and Gaussian (s,t)-Pell-Lucas...
SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3
SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3
In
this study, we study on special Pell and Pell Lucas matrices of order 3x3, entries of whose nth powers are related specific Pell and Pell Lucas
numbers with indices certain posi...
Almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers
Almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers
In this work, the general terms of almost balancers, almost cobalancers, almost Lucas-balancers and almost Lucas-cobalancers of first and second type are determined in terms of bal...