scholarly journals Pell numbers whose Euler function is a Pell number

2017 ◽  
Vol 101 (115) ◽  
pp. 231-245
Author(s):  
Bernadette Faye ◽  
Florian Luca
Keyword(s):  
Euler Function ◽  
Pell Numbers ◽  
Pell Number

We show that the only Pell numbers whose Euler function is also a Pell number are 1 and 2.

scholarly journals Gaussian Pell Numbers

2018 ◽  
Vol 7 (4.10) ◽  
pp. 1012
Author(s):  
P. Balamurugan ◽  
A. Gnanam
Keyword(s):  
Recurrence Relation ◽  
Complex Plane ◽  
Complex Numbers ◽  
Two Dimensional ◽  
Dimensional Approach ◽  
Pell Numbers ◽  
Pell Number

Gaussian numbers means representation as Complex numbers. In this work, Gaussian Pell numbers are defined from recurrence relation of Pell numbers. Here the recurrence relation on Gaussian Pell number is represented in two dimensional approach. This provides an extension of Pell numbers into the complex plane. 

There are no Diophantine quadruples of Pell numbers

2021 ◽  
pp. 1-19
Author(s):  
Salah Eddine Rihane ◽  
Florian Luca ◽  
Alain Togbé
Keyword(s):  
Positive Integer ◽  
Pell Numbers ◽  
Pell Number ◽  
Diophantine Quadruples ◽  
Positive Integers

In this paper, we prove that there are no positive integers [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] such that [Formula: see text] is a Diophantine quadruple, where for a positive integer [Formula: see text], [Formula: see text] is the [Formula: see text]th Pell number.

scholarly journals On Generalized Pell Numbers of Order r ≥ 2

2021 ◽  
Vol 22 (1) ◽  
pp. 125-138
Author(s):  
E. V. Pereira Spreafico ◽  
M. Rachidi
Keyword(s):  
Linear Combination ◽  
Fundamental System ◽  
Analytic Study ◽  
Pell Numbers ◽  
Pell Number

In this paper we investigate the generalized Pell numbers of order r ≥ 2 through the properties of their related fundamental system of generalized Pell numbers. That is, the generalized Pell number of order r ≥ 2; are expressed as a linear combination of a fundamental system of generalized Pell numbers. The properties of this fundamental system are examined and results can be established for generalized Pell numbers of order r ≥ 2. Some identities and combinatorial results are established. Moreover, the analytic study of the fundamental system of generalized Pell is provided. Furthermore, the generalized Pell Cassini identity type is provided.

scholarly journals On Pillai's problem with Pell numbers and powers of 2

2019 ◽  
Author(s):  
Mohand Ouamar Hernane ◽  
Florian Luca ◽  
Salah Rihane ◽  
Alain Togbé
Keyword(s):  
Pell Numbers ◽  
Powers Of 2 ◽  
International Audience ◽  
Pell Number

International audience In this paper, we find all integers c having at least two representations as a difference between a Pell number and a power of 2.

On circulant like matrices properties involving Horadam, Fibonacci, Jacobsthal and Pell numbers

2021 ◽  
Vol 617 ◽  
pp. 100-120
Author(s):  
Enide Andrade ◽  
Dante Carrasco-Olivera ◽  
Cristina Manzaneda
Keyword(s):  
Pell Numbers

scholarly journals Enumeration of Standard Young Tableaux of Shifted Strips with Constant Width

10.37236/6466 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Ping Sun
Keyword(s):  
Integral Method ◽  
Recurrence Relations ◽  
Young Tableau ◽  
Constant Width ◽  
Young Tableaux ◽  
Pell Number ◽  
Standard Young Tableaux ◽  
Standard Young Tableau

Let $g_{n_1,n_2}$ be the number of standard Young tableau of truncated shifted shape with $n_1$ rows and $n_2$ boxes in each row. By using the integral method this paper derives the recurrence relations of $g_{3,n}$, $g_{n,4}$ and $g_{n,5}$ respectively. Specifically, $g_{n,4}$ is the $(2n-1)$-st Pell number.

Pell Numbers, Pell–Lucas Numbers and Modular Group

2007 ◽  
Vol 14 (01) ◽  
pp. 97-102 ◽  
Author(s):  
Q. Mushtaq ◽  
U. Hayat
Keyword(s):  
Modular Group ◽  
Symmetric Matrix ◽  
Lucas Numbers ◽  
Lucas Number ◽  
Pell Numbers ◽  
The Matrix

We show that the matrix A(g), representing the element g = ((xy)2(xy2)2)m (m ≥ 1) of the modular group PSL(2,Z) = 〈x,y : x2 = y3 = 1〉, where [Formula: see text] and [Formula: see text], is a 2 × 2 symmetric matrix whose entries are Pell numbers and whose trace is a Pell–Lucas number. If g fixes elements of [Formula: see text], where d is a square-free positive number, on the circuit of the coset diagram, then d = 2 and there are only four pairs of ambiguous numbers on the circuit.

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