• Korean Journal of Mathematics
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• v.31 no.1
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• pp.63-73
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• 2023

In this paper, we determine all repdigits, which are difference of two Pell and Pell-Lucas numbers. It is shown that the largest repdigit which is difference of two Pell numbers is 99 = 169 - 70 = P₇ - P₆ and the largest repdigit which is difference of two Pell-Lucas numbers is 444 = 478 - 34 = Q₇ - Q₄.

• Honam Mathematical Journal
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• v.45 no.4
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• pp.572-584
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• 2023

In this study, we search for Pell and Pell-Lucas numbers, which are concatenations of two repdigits and find these numbers to be only 12, 29, 70 and 14, 34, 82, respectively. We use Baker's Theory and Baker-Davenport basis reduction method while finding the solutions.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.243-257
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• 2022

In this paper, we present and prove an new theorem on symmetric functions. By using this theorem, we derive some new generating functions of the products of (p, q)-Fibonacci numbers, (p, q)-Lucas numbers, (p, q)-Pell numbers, (p, q)-Pell Lucas numbers, (p, q)-Jacobsthal numbers and (p, q)-Jacobsthal Lucas numbers with Chebyshev polynomials of the first kind.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.97-111
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• 2019

The purpose of work is to study the sums of k distanced numbers in Pell sequence {$P_i$} as well as in the generalized ${\lambda}-Pell$ sequence {$P_{{\lambda},i}$}.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.197-206
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• 2019

We consider the extended generalized Hecke groups ${\bar{H}}_{3,q}$ generated by $X(z)=-(z-1)^{-1}$, $Y(z)=-(z+{\lambda}_q)^{-1}$ with ${\lambda}_q=2\;cos({\frac{\pi}{q}})$ where $q{\geq}3$ an integer. In this work, we study the generalized Pell sequences in ${\bar{H}}_{3,q}$. Also, we show that the entries of the matrix representation of each element in the extended generalized Hecke Group ${\bar{H}}_{3,3}$ can be written by using Pell, Pell-Lucas and modified-Pell numbers.