Results 11 to 20 of about 83 (68)
Lucas sequences and repdigits [PDF]
Mathematica Bohemica, 2021 Summary: Let \((G_{n})_{n\geq 1}\) be a binary linear recurrence sequence that is represented by the Lucas sequences of the first and second kind, which are \(\{U_n\}\) and \(\{V_n\}\), respectively. We show that the Diophantine equation \(G_n=B\cdot(g^{lm}-1)/(g^{l}-1)\) has only finitely many solutions in \(n,m\in\mathbb{Z}^+\), where \(g\geq 2 ...
Hayder Raheem Hashim, Szabolcs Tengely
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Repdigits as Euler functions of Lucas numbers [PDF]
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2016 Abstract We prove some results about the structure of all Lucas numbers whose Euler function is a repdigit in base 10. For example, we show that if L n is such a Lucas number, then n < 10 111 is of the form p or p
Bravo Jhon J. +3 more
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Repdigits in the base $b$ as sums of four balancing numbers [PDF]
Mathematica Bohemica, 2021 The sequence of balancing numbers $(B_n)$ is defined by the recurrence relation $B_n=6B_{n-1}-B_{n-2}$ for $n\geq2$ with initial conditions $B_0=0$ and $B_1=1.$ $B_n$ is called the $n$th balancing number. In this paper, we find all repdigits in the base $
Refik Keskin, Fatih Erduvan
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Repdigits in generalized Pell sequences [PDF]
Archivum Mathematicum, 2020 In this paper, the authors study the \(k\)-generalized Pell sequence, which starts with \(0,\ldots,0,1\) and satisfies the recurrence \(P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)}\). They find all \(k\)-generalized Pell numbers which are repdigits, namely \(P_5^{(3)}=33\) and \(P_6^{(4)}=88\).
Bravo, Jhon J., Herrera, Jose L.
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Repdigits as difference of two Fibonacci or Lucas numbers
Математичні Студії, 2021 In the present study we investigate all repdigits which are expressed as a difference of two Fibonacci or Lucas numbers. We show that if $F_{n}-F_{m}$ is a repdigit, where $F_{n}$ denotes the $n$-th Fibonacci number, then $(n,m)\in \{(7,3),(9,1),(9,2 ...
P. Ray, K. Bhoi
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Mathematics of Computation, 2013 For a positive integer \(n\) let \(\sigma(n)\) denote the sum of divisors of \(n\). The number \(n\) is called perfect if \(\sigma(n) = 2n\). It is not known if there are infinitely many perfect numbers. For an integer \(g > 1\) a repdigit in base \(g\) is a positive integer \(N\) all of whose base \(g\) digits are the same.
Kevin A. Broughan +2 more
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Pentagonal and heptagonal repdigits [PDF]
Annales Mathematicae et Informaticae, 2020 Summary: In this paper, we prove a finiteness theorem concerning repdigits represented by a fixed quadratic polynomial. We also show that the only pentagonal numbers which are also repdigits are 1, 5 and 22. Similarly, the only heptagonal numbers which are repdigits are 1, 7 and 55.
Kafle, Bir, Luca, Florian, Togbé, Alain
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Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences
Mathematics, 2023 In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the k-generalized Fibonacci sequence which are almost repdigits. In particular, we find all k-
Alaa Altassan, Murat Alan
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Factorials as repdigits in base $b$ [PDF]
Notes on Number Theory and Discrete Mathematics, 2022 Let $b\in \left\{ 2,3, \ldots,9\right\}.$ In this paper, we show that the solutions of the equation $\left( x\right) _{b}=m! $ are $\left( 11\right) _{5}=3!, \left( 33\right) _{7}=\left( 44\right)_{5}=4!$, where $\left( x\right) _{b}$ has at least two digits.
Nurettin Irmak, Alain Togbé
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Padovan Numbers as Sum of Two Repdigits
Proceedings of the Bulgarian Academy of Sciences, 2023 Padovan sequence $$(P_{n})$$ is given by $$P_{n}=P_{n-2}+P_{n-3}$$ for $$n\geq3$$ with initial condition $$(P_{0},P_{1},P_{2})=(1,1,1)$$. A positive integer is called a repdigit if all of its digits are equal. In this study, we examine the terms of the Padovan sequence, which are the sum of two repdigits.
Duman, Merve Güney +5 more
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