• 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 for History of Mathematics
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• v.31 no.4
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• pp.183-196
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• 2018

In this study, we propose an approximate method to make Jisuguimundo with magic number 93 to 109. In this method, for two numbers p, q with a relationship of M = 2p+q, we use eight pairs of two numbers with sum p and five pairs of two numbers with sum q. Such numbers must be between 1 and 30. Instead of determining all positions of thirty numbers, this method shows that Jisuguimundo with magic number 93 to 109 can be made by determining positions of thirteen numbers $a_i$(i = 1, 2, ${\cdots}$, 8), $b_5$, $c_i$(i = 1, 2, 3, 4). Method 1 is used to make Jisuguimundo with magic number 93 to 108, and method 2 is used to make Jisuguimundo with magic number 109.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1079-1095
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• 2021

In this paper, we give new congruences with the generalized Catalan numbers and harmonic numbers modulo p². One of our results is as follows: for prime number p > 3, $${\sum\limits_{k=(p+1)/2}^{p-1}}\;k^2B_{p,k}B_{p,k-(p-1)/2}H_k{\equiv}(-1)^{(p-1)/2}\(-{\frac{521}{36}}p-{\frac{1}{p}}-{\frac{41}{12}}+pH^2_{3(p-1)/2}-10pq^2_p(2)+4\({\frac{10}{3}}p+1\)q_p(2)\)\;(mod\;p^2),$$ where q_p(2) is Fermat quotient.

• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.197-209
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• 2023

In this paper, the generalized (p, q)-poly-Genocchi polynomials with variable a is defined by generalizing it more, and various properties of this polynomial are introduced. To do this, we define a generating function and use the definition to introduce some interesting properties as follows: basic properties, relation between Stirling numbers of the second kind and generalized (p, q)-poly-Genocchi polynomials with variable a and symmetric properties.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.221-231
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• 2022

In this paper, we study differential equations arising from the generating functions of (p, q)-Hermite polynomials. We use this differential equation to give explicit identities for (p, q)-Hermite polynomials.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.21-30
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• 2000

We give a proof of the distribution relation for q-Bernoulli polynomials $B_{k}$(x : q) by using q-integral and evaluate the values of p-adic q-L-function.n.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.1-12
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• 2007

In this paper, we consider the q-Volkenborn integral of uniformly differentiable functions on the p-adic integer ring. By using this integral, we obtain the generating functions of twisted q-generalized Bernoulli numbers and polynomials. We find some properties of these numbers and polynomials.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.423-438
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• 2012

In this paper, we discuss numbers of downwards and upwards in generalized paper folding sequences. We compute the exact number of downwards and upwards in $R^n_p$ and $(R_pR_q)^n$ by using the properties of recursive sequences where n, p and q are natural numbers with $p{\geq}2$ and $q{\geq}2$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.4
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• pp.1149-1156
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• 2016

In this paper, we introduce the degenerate Carlitz q-Bernoulli numbers and polynomials and give some interesting identities and properties of these numbers and polynomials which are derived from the generating functions and p-adic integral equations.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.395-406
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• 2013

Generalized paper folding sequences $X^n_p$ and $(X_pY_q)^n$ where $X,Y{\in}\{R,L,U,D\}$, and $n,p,q{\in}\mathbb{N}$, and with $p,q{\geq}2$ are classified in this paper. We show that all generalized paper folding sequences $X^n_p$ are classified into one type if we classify generalize paper folding sequences along with the numbers of downwards and upwards. In addition, we investigate the numbers of downwards and upwards in $(X_pY_q)^n$ and prove that all generalized paper folding sequences $(X_pY_q)^n$ are classified into two types.