On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3
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DOI: 10.1142/s1793042120500876
Abstract: For an integer [Formula: see text], let [Formula: see text] be the [Formula: see text]-generalized Fibonacci sequence which starts with [Formula: see text] (a total of [Formula: see text] terms) and for which each term… read more here.
Keywords: fibonacci numbers; generalized fibonacci; problem pillai; formula see ... See more keywords
Eventually monotonic solutions of the generalized Fibonacci equations
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DOI: 10.1515/math-2025-0198
Abstract: Abstract The purpose of this work is, for the first time, to introduce some results about the eventually monotonic solutions of the generalized Fibonacci equations. In addition, some concrete examples are given to illustrate the… read more here.
Keywords: monotonic solutions; solutions generalized; eventually monotonic; fibonacci equations ... See more keywords
Diophantine quadruples with values in k-generalized Fibonacci numbers
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DOI: 10.1515/ms-2017-0156
Abstract: Abstract We consider for integers k ≥ 2 the k–generalized Fibonacci sequences F(k) := (Fn(k))n≥2−k, $\begin{array}{} (F_n^{(k)})_{n\geq 2-k}, \end{array} $ whose first k terms are 0, …, 0, 1 and each term afterwards is the… read more here.
Keywords: quadruples values; fibonacci numbers; generalized fibonacci; diophantine quadruples ... See more keywords
A Two-by-Two matrix representation of a generalized Fibonacci sequence
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DOI: 10.15672/hjms.2017.477
Abstract: The Fibonacci sequence is a well-known example of second order recurrence sequence, which belongs to a particular class of recursive sequences. In this article, other generalized Fibonacci sequence is introduced and defined by $ H_{k,n+1}=2H_{k,n}+kH_{k,n-1},~n\geq1,~H_{k,0}=2,~H_{k,1}=1$… read more here.
Keywords: matrix representation; fibonacci sequence; generalized fibonacci; two two ... See more keywords
Solutions of Some Diophantine Equations in terms of Generalized Fibonacci and Lucas Numbers
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DOI: 10.15672/hjms.2017.527
Abstract: In this study, we present some identities involving generalized Fibonacci sequence $\left(U_{n}\right)$ and generalized Lucas sequence $\left(V_{n}\right)$. Then we give all solutions of the Diophantine equations $x^{2}-V_{n}xy+(-1)^{n}y^{2}=\pm (p^{2}+4)U_{n}^{2},$ $x^{2}-V_{n}xy+(-1)^{n}y^{2}=\pm U_{n}^{2},$ $x^{2}-(p^{2}+4)U_{n}xy-(p^{2}+4)(-1)^{n}y^{2}=\pm V_{n}^{2},$ $x^{2}-V_{n}xy\pm y^{2}=\pm 1,$… read more here.
Keywords: left right; equations terms; generalized fibonacci; solutions diophantine ... See more keywords
On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations
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DOI: 10.3390/math12081156
Abstract: This paper presents a comprehensive survey of the generalization of hybrid numbers and hybrid polynomials, particularly in the fields of mathematics and physics. In this paper, by using higher-order generalized Fibonacci polynomials, we introduce higher-order… read more here.
Keywords: higher order; order generalized; fibonacci hybrinomials; recurrence ... See more keywords
On the Solutions of Quaternion Difference Equations in Terms of Generalized Fibonacci-Type Numbers
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DOI: 10.3390/sym14102190
Abstract: The aim of this paper is to investigate the solution of the following difference equation zn+1=(pn)−1,n∈N0,N0=N∪0 where pn=a+bzn+czn−1zn with the parameters a, b, c and the initial values z−1,z0 are nonzero quaternions such that their… read more here.
Keywords: difference equations; fibonacci type; type numbers; generalized fibonacci ... See more keywords