• 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.

• 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.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.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.535-547
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• 2019

In this paper, by using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and $Peth{\ddot{o}}$, we find all generalized Fibonacci numbers which are Pell numbers. This paper continues a previous work that searched for Pell numbers in the Fibonacci sequence.

• 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.

• 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.34 no.3
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• pp.209-219
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• 2021

A set {a₁, a₂, ⋯ , a_m} of positive integers is called a Diophantine m-tuple if a_ia_j + 1 is a perfect square for all 1 ≤ i < j ≤ m. Let F_n be the nth Fibonacci number which is defined by F₀ = 0, F₁ = 1 and F_n+2 = F_n+1 + F_n. In this paper, we find the extendibility of Diophantine pairs {F_2k, b} with some conditions.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.327-334
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• 2021

In this paper, we find all the prime numbers p that satisfy the following statement. If a positive integer k is a divisor of p - 1, then there is a sequence consisting of all k-th power residues modulo p, satisfying the recurrence equation of the Fibonacci sequence modulo p.

• Journal of the Korean Mathematical Society
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• v.55 no.2
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• pp.425-445
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• 2018

A set {$a_1,\;a_2,{\ldots},\;a_m$} of positive integers is called a Diophantine m-tuple if $a_ia_j+1$ is a perfect square for all $1{\leq}i$ < $j{\leq}m$. In this paper, we show that the form of third element in Diophantine pairs and develop some results which are needed to prove the extendibility of the Diophantine pair {a, b} with some conditions. By using this result, we prove the extendibility of Diophantine pairs {$F_{k-2}F_{k+1},\;F_{k-1}F_{k+2}$} and {$F_{k-2}F_{k-1},\;F_{k+1}F_{k+2}$}, where $F_n$ is the n-th Fibonacci number.