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Random walk on a discrete Heisenberg group
We use the estimate of paths in Z 2 enclosing a null algebraic area to compute correction terms on the random walk on certain discrete Heisenberg...
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On m-step Fibonacci sequence in discrete Lotka-Volterra system
The integrable Lotka-Volterra (LV) system stands for a prey-predator model in mathematical biology. The discrete LV (dLV) system is derived from a...
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Fibonacci and Lucas congruences and their applications
In this paper we obtain some new identities containing Fibonacci and Lucas numbers. These identities allow us to give some congruences concerning...
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On sums related to the numerator of generating functions for the kth power of Fibonacci numbers on sums related to the numerator of generating functions for the kth power of Fibonacci numbers
New results about some sums s n ( k, l ) of products of the Lucas numbers, which are of similar type as the sums in [SEIBERT, J.—TROJOVSK Ý, P.: On...
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Regular modules and quasi-lengths over a 3-Kronecker quiver: using Fibonacci numbers
Let Q be a 3-Kronecker quiver (i.e., two vertices and three arrows having the same starting and ending vertices). The dimension vectors of the...
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Fibonacci lattice points
Odd indexed Fibonacci numbers F2n+1 can be written as sums of two squares a 2 + b 2 . In this paper, we study the distribution of the lattice points ( a , b ...
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On the diophantine equation X 2 − (1 + a 2)Y 4 = −2a
Let a ⩾ 1 be an integer. In this paper, we will prove the equation in the title has at most three positive integer solutions.
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Tribonacci partition formulas modulo m
Each Tribonacci sequence starting with an arbitrary triple of integers is periodic modulo m for any modulus m > 1. For a given m , the map** between...
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Periodic harmonic functions on lattices and points count in positive characteristic
This survey deals with pluri-periodic harmonic functions on lattices with values in a field of positive characteristic. We mention, as a motivation,...
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Divisibity, iterated digit sums, primality tests
The divisibility of numbers is obtained by iteration of the weighted sum of their integer digits. Then evaluation of the related congruences yields...
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Criteria for testing Wall’s question
In this paper we find certain equivalent formulations of Wall’s question and derive two interesting criteria that can be used to resolve this...
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Noncirculant Toeplitz matrices all of whose powers are Toeplitz
Let a, b and c be fixed complex numbers. Let M n ( a, b, c ) be the n × n Toeplitz matrix all of whose entries above the diagonal are a , all of whose...
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On the universal zero attractor of the Tribonacci-related polynomials
In this paper we solve a conjecture on the zeros of R -Bonacci polynomials in the case when r =3 (Tribonacci polynomials) and determine the zero...
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Fibonacci Numbers and Equilibria in Large “Neighborhood” Games
We deal with a game-theoretic framework involving a finite number of infinite populations, members of which have a finite number of available...
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Power Classes Of Recurrence Sequences
In this note, we improve upon a result from [4] concerning q -power classes of linearly recurrent sequences with a dominant root.
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Square-free Lucas d-pseudoprimes and Carmichael-Lucas numbers
Let d be a fixed positive integer. A Lucas d -pseudoprime is a Lucas pseudoprime N for which there exists a Lucas sequence U ( P, Q ) such that the rank...
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Convolution Equations on Lattices: Periodic Solutions with Values in a Prime Characteristic Field
These notes are inspired by the theory of cellular automata. The latter aims, in particular, to provide a model for inter-cellular or inter-molecular...
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Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences
In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2 n + y 2 n , n ∈ ℕ, are studied....