Pell and Pell-Lucas numbers of the form
Yunyun Qu, Jiwen Zeng (2020)
Czechoslovak Mathematical Journal
Similarity:
In this paper, we find all Pell and Pell-Lucas numbers written in the form , in nonnegative integers , , , with .
Yunyun Qu, Jiwen Zeng (2020)
Czechoslovak Mathematical Journal
Similarity:
In this paper, we find all Pell and Pell-Lucas numbers written in the form , in nonnegative integers , , , with .
Jian-Ping Fang (2016)
Czechoslovak Mathematical Journal
Similarity:
We derive two identities for multiple basic hyper-geometric series associated with the unitary group. In order to get the two identities, we first present two known -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two -Chu-Vandermonde summations established by Milne, we arrive at our results. Using the identities obtained in this paper, we give two interesting identities involving binomial...
Takao Komatsu (2002)
Bulletin de la Société Mathématique de France
Similarity:
Let be irrational. Several authors studied the numbers where is a positive integer and denotes the set of all real numbers of the form with restricted integer coefficients . The value of was determined for many particular Pisot numbers and for the golden number. In this paper the value of is determined for irrational numbers , satisfying with a positive integer .
Victor J. W. Guo (2018)
Czechoslovak Mathematical Journal
Similarity:
We give a new and elementary proof of Jackson’s terminating -analogue of Dixon’s identity by using recurrences and induction.
Fabien Durand (2011)
Journal of the European Mathematical Society
Similarity:
The seminal theorem of Cobham has given rise during the last 40 years to a lot of work about non-standard numeration systems and has been extended to many contexts. In this paper, as a result of fifteen years of improvements, we obtain a complete and general version for the so-called substitutive sequences. Let and be two multiplicatively independent Perron numbers. Then a sequence , where is a finite alphabet, is both -substitutive and -substitutive if and only if is ultimately...
Jhon J. Bravo, Jose L. Herrera (2020)
Archivum Mathematicum
Similarity:
For an integer , let be the generalized Pell sequence which starts with ( terms) and each term afterwards is given by the linear recurrence . In this paper, we find all -generalized Pell numbers with only one distinct digit (the so-called repdigits). Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for repdigits in the usual Pell sequence . ...
Sheng-Liang Yang, Yan-Xue Xu, Tian-Xiao He (2017)
Czechoslovak Mathematical Journal
Similarity:
For integers , Brietzke (2008) defined the -central coefficients of an infinite lower triangular matrix as , with , and the -central coefficient triangle of as It is known that the -central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array with and , we obtain the generating function of its -central coefficients and give an explicit representation for the -central Riordan array in terms of the Riordan array ....
I. Kiuchi, M. Minamide, Y. Tanigawa (2015)
Acta Arithmetica
Similarity:
Let be the Ramanujan sum, i.e. , where μ is the Möbius function. In a paper of Chan and Kumchev (2012), asymptotic formulas for (k = 1,2) are obtained. As an analogous problem, we evaluate (k = 1,2), where .
Joseph Kupka
Similarity:
CONTENTS1. Introduction...................................................................................................... 52. Notation and basic terminology........................................................................... 73. Definition and basic properties of the spaces................................. 114. Integral representation of bounded linear functionals on ........ 235. Examples in theory...................................................................................
S. Driss (2015)
Discussiones Mathematicae - General Algebra and Applications
Similarity:
Let be a finite field and . The aim of this paper is to prove that the length of the continued fraction expansion of , is bounded.
Ahmed Boughammoura, Yousra Braham (2021)
Czechoslovak Mathematical Journal
Similarity:
In this work we consider a diffusion problem in a periodic composite having three phases: matrix, fibers and interphase. The heat conductivities of the medium vary periodically with a period of size ( and ) in the transverse directions of the fibers. In addition, we assume that the conductivity of the interphase material and the anisotropy contrast of the material in the fibers are of the same order (the so-called double-porosity type scaling) while the matrix material has a conductivity...
Hans Triebel (1994)
Studia Mathematica
Similarity:
Let , where the sum is taken over the lattice of all points k in having integer-valued components, j∈ℕ and . Let be either or (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on The aim of the paper is to clarify under what conditions is equivalent to .
Reynaldo Rojas-Hernández (2015)
Commentationes Mathematicae Universitatis Carolinae
Similarity:
We show that any -product of at most -many -spaces has the -property. This result generalizes some known results about -spaces. On the other hand, we prove that every -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...
Ananga Kumar Das, Pratibha Bhat, Ria Gupta (2016)
Mathematica Bohemica
Similarity:
The notion of -normality was introduced and studied by Arhangel’skii, Ludwig in 2001. Recently, almost -normal spaces, which is a simultaneous generalization of -normal and almost normal spaces, were introduced by Das, Bhat and Tartir. We introduce a new generalization of normality, namely weak -normality, in terms of -closed sets, which turns out to be a simultaneous generalization of -normality and -normality. A space is said to be weakly -normal (w-normal if for every...
Vladimir Petrov Kostov (2019)
Mathematica Bohemica
Similarity:
By Descartes’ rule of signs, a real degree polynomial with all nonvanishing coefficients with sign changes and sign preservations in the sequence of its coefficients () has positive and negative roots, where and . For , for every possible choice of the sequence of signs of coefficients of (called sign pattern) and for every pair satisfying these conditions there exists a polynomial with exactly positive and exactly negative roots (all of them simple). For ...