Results 31 to 40 of about 3,575 (254)

On Homogeneous Combinations of Linear Recurrence Sequences

Mathematics, 2020
Let (Fn)n≥0 be the Fibonacci sequence given by Fn+2=Fn+1+Fn, for n≥0, where F0=0 and F1=1. There are several interesting identities involving this sequence such as Fn2+Fn+12=F2n+1, for all n≥0. In 2012, Chaves, Marques and Togbé proved that if (Gm)m is a
Marie Hubálovská, Štěpán Hubálovský, Eva Trojovská   +2 more
doaj   +1 more source

Fibonacci Numbers with a Prescribed Block of Digits

Mathematics, 2020
In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of algebraic numbers and some tools from ...
Pavel Trojovský
doaj   +1 more source

Linear forms in two logarithms and Schneider's method

Mathematische Annalen, 1978
Maurice Mignotte, Michel Waldschmidt, Mignotte Maurice   +2 more
exaly   +3 more sources

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
doaj   +1 more source

Estimates of linear forms in logarithms

, 1986

core   +2 more sources

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
doaj   +1 more source

Solutions of the Diophantine Equations Br=Js+Jt and Cr=Js+Jt

Journal of Mathematics, 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.
Ahmed Gaber, Mohiedeen Ahmed
doaj   +1 more source

Products of Factorials in Smarandache Type Expressions [PDF]

, 1997
The proof of Theorem 1 uses lower bounds for linear forms in logarithms of algebraiC numbers (see [1] and [7]) as well as an idea of Stewart (see [10])
Luca, Florian
core   +1 more source

Padovan numbers which are concatenations of three Padovan or Perrin numbers [PDF]

Notes on Number Theory and Discrete Mathematics
This paper presents all Padovan numbers that can be written as the concatenation of three Padovan or Perrin numbers under a certain constraint. Namely, we consider the Diophantine equations Pₜ=10ᵈ⁺ˡPₘ+10ˡPₙ+Pᵣ and Pₜ=10ᵈ⁺ˡRₘ+10ˡRₙ+Rᵣ, where k,m,n,r,d and
Fatih Erduvan
doaj   +1 more source

The extensibility of the Diophantine triple {2, b, c}

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple.
Adžaga Nikola, Filipin Alan, Jurasić Ana   +2 more
doaj   +1 more source