Results 21 to 30 of about 83 (68)
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 tribonacci number modulo 9 to deal with three individual cases.
Yuetong Zhou +3 more
openaire +1 more source
On the Euler function of repdigits [PDF]
Czechoslovak Mathematical Journal, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
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
doaj +1 more source
Integers, 2016 A \emph{repdigit} is a natural number greater than 10 which has all of its base-10 digits the same. In this paper we find all examples of two repdigits adding to a square. The proofs lead to interesting questions about consecutive quadratic residues and non-residues, and provide an elementary application of elliptic curves.
Bart Goddard, Jeremy Rouse
openaire +4 more sources
Perrin numbers and distinct repdigits [PDF]
, 2020 We determine all Perrin numbers that are concatenations of two repdigits.
Mahadi Ddamulira, Toboka Chalebgwa
openaire +1 more source
On repdigits as product of $k$-Fibonacci and $k$-Lucas numbers [PDF]
Mathematica BohemicaFor an integer $k\geq2$, let $(F_n^{(k)})_{n\geq-(k-2)}$, $(L_n^{(k)})_{n \geq-(k-2)}$ be $k$-Fibonacci and $k$-Lucas sequences, respectively. For these sequences the first $k$ terms are $0,\ldots,0,1$ and $0,\ldots,0,2,1$, respectively, and each term ...
Safia Seffah +2 more
doaj +1 more source
Repdigits in k-Lucas sequences
Proceedings - Mathematical Sciences, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bravo, Jhon J., Luca, Florian
openaire +1 more source
On Repdigits as Sums of Fibonacci and Tribonacci Numbers [PDF]
Symmetry, 2020 In this paper, we use Baker’s theory for nonzero linear forms in logarithms of algebraic numbers and a Baker-Davenport reduction procedure to find all repdigits (i.e., numbers with only one distinct digit in its decimal expansion, thus they can be seen as the easiest case of palindromic numbers, which are a ”symmetrical” type of numbers) that can be ...
openaire +1 more source
A Diophantine equation in $k$-Fibonacci numbers and repdigits [PDF]
Colloquium Mathematicum, 2018 Summary: The \(k\)-generalized Fibonacci sequence \(\{F_{n}^{(k)}\}_{n}\) starts with the \(k\) values \(0,\dots ,0,1\) and each term afterwards is the sum of the \(k\) preceding terms. We study which members of this sequence are sums of two repdigts, extending a result of \textit{S. Díaz Alvarado} and \textit{F. Luca} [Aportaciones Mat., Investig. 20,
Bravo, J. +2 more
openaire +3 more sources
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 Tribonacci number (both with the same indexes).
Dušan Bednařík, Eva Trojovská
openaire +2 more sources