Results 11 to 20 of about 161 (91)
Repdigits as Product of Fibonacci and Tribonacci Numbers [PDF]
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 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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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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Repdigits as Euler functions of Lucas numbers [PDF]
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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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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Narayana numbers as products of three repdigits in base g [PDF]
Acta et Commentationes Universitatis Tartuensis de Mathematica, 2023 In this paper, we show that there are only finitely many Narayana's numbers which can be written as a product of three repdigits in base g with g >= 2. Moreover, for 2 <= g <= 10, we determine all these numbers.
Pagdame Tiebekabe +2 more
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Repdigits as Sums of Four Tribonacci Numbers [PDF]
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 tribonacci number modulo 9 to deal with three individual cases.
Yuetong Zhou +3 more
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On the Euler function of repdigits [PDF]
Czechoslovak Mathematical Journal, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luca, Florian
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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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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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