Results 11 to 20 of about 111 (68)
Repdigits as Product of Fibonacci and Tribonacci Numbers
Mathematics, 2020 In this paper, we study the problem of the explicit intersection of two sequences. More specifically, we find all repdigits (i.e., numbers with only one repeated digit in its decimal expansion) which can be written as the product of a Fibonacci by a ...
Dušan Bednařík, Eva Trojovská
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Repdigits as Euler functions of Lucas numbers
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 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 Ln is such a Lucas number, then n < 10111 is of the form p or p2, where p3 | 10p-1 -1.
Bravo Jhon J. +3 more
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Repdigits as sums of three Padovan numbers. [PDF]
Bol Soc Mat Mex, 2020 International audienceLet $ \{P_{n}\}_{n\geq 0} $ be the sequence of Padovan numbers defined by $ P_0=0 $, $ P_1 =1=P_2$, and $ P_{n+3}= P_{n+1} +P_n$ for all $ n\geq 0 $. In this paper, we find all repdigits in base $ 10 $ which can be written as a sum
Ddamulira M.
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Pentagonal and heptagonal repdigits [PDF]
, 2020 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.
Luca, Florian, Togbé, Alain, Kafle, Bir
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Solutions of the Diophantine Equations Br = Js + Jt and Cr = Js + Jt
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 Let Brr≥0, Jrr≥0, and Crr≥0 be the balancing, Jacobsthal, and Lucas balancing numbers, respectively. In this paper, the diophantine equations Br = Js + Jt and Cr = Js + Jt are completely solved. The solutions rely basically on Matveev’s theorem on linear forms in logarithms of algebraic numbers and a procedure of reducing the upper bound due to Dujella
Ahmed Gaber +2 more
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Can a Lucas number be a sum of three repdigits? [PDF]
, 2020 summary:We give the answer to the question in the title by proving that \begin{equation*} L_{18} = 5778 = 5555 + 222 + 1 \end{equation*} is the largest Lucas number expressible as a sum of exactly three repdigits.
Adegbindin, Chèfiath A., Togbé, Alain
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Padovan numbers as difference of two repdigits
, 2023 In this paper, we find all Padovan numbers which can be written as are difference of two repdigits. It is shown that all Padovan numbers which can be written as a difference of two repdigits are P-k is an element of {2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37,
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Almost repdigits in balancing and Lucas-balancing sequences [PDF]
Notes on Number Theory and Discrete MathematicsIn 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 balancing and Lucas-balancing sequences which are almost repdigits.
Manasi K. Sahukar, Hussain Basha
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On b-repdigit polygonal numbers [PDF]
Notes on Number Theory and Discrete MathematicsWe prove a finiteness theorem concerning repdigits in base b≥2 represented by a fixed quadratic polynomial. We also show that there is a finite number of polygonal numbers that are also b-repdigits for all b≥2 provided that (b,s) ∈\ {((8(s-2)/(s-4))(d+1),
Adriana Mora, Eric Bravo
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k-generalized Fibonacci numbers which are concatenations of two repdigits
, 2021 We show that the k-generalized Fibonacci numbers that are concatenations of two repdigits have at most four ...
Alahmadi, Adel +7 more
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