Results 11 to 20 of about 109 (79)
Repdigits as Sums of Four Tribonacci Numbers
Symmetry, 2022 In this paper, we show that 66666 is the largest repdigit expressible as the sum of four tribonacci numbers. We used Binet’s formula, Baker’s theory, and a reduction method during the proving procedure. We also used the periodic properties of
Yuetong Zhou +3 more
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On repdigits as product of consecutive Lucas numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2018 Let (L-n)(n >= 0 )be the Lucas sequence. D. Marques and A. Togbe [7] showed that if F-n . . . Fn+k-1 is a repdigit with at least two digits, then (k, n) = (1, 10), where (F-n)(>= 0) is the Fibonacci sequence. In this paper, we solve the equation L-n . . .
Irmak, Nurettin, Togbe, Alain
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On Sierpiński and Riesel Repdigits and Repintegers
For positive integers b≥2 ...
Pontes, Kaelyn +5 more
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Repdigits as sums of three Padovan numbers. [PDF]
Bol Soc Mat Mex, 2020 AbstractLet $$ \{P_{n}\}_{n\ge 0} $${Pn}n≥0 be the sequence of Padovan numbers defined by $$ P_0=0 $$P0=0, $$ P_1 =1=P_2$$P1=1=P2, and $$ P_{n+3}= P_{n+1} +P_n$$Pn+3=Pn+1+Pn for all $$ n\ge 0 $$n≥0. In this paper, we find all repdigits in base 10 which can be written as a sum of three Padovan numbers.
Ddamulira M.
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Tribonacci numbers that are concatenations of two repdigits. [PDF]
Rev R Acad Cienc Exactas Fis Nat A Mat, 2020 Let $ (T_{n})_{n\ge 0} $ be the sequence of Tribonacci numbers defined by $ T_0=0 $, $ T_1=T_2=1$, and $ T_{n+3}= T_{n+2}+T_{n+1} +T_n$ for all $ n\ge 0 $. In this note, we use of lower bounds for linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction procedure to find all Tribonacci numbers that are concatenations of two ...
Ddamulira M.
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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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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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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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