Results 1 to 10 of about 13,182 (153)
p-adic difference-difference Lotka-Volterra equation and ultra-discrete limit [PDF]
International Journal of Mathematics and Mathematical Sciences, 2001 We study the difference-difference Lotka-Volterra equations in p-adic number space and its p-adic valuation version. We point out that the structure of the space given by taking the ultra-discrete limit is the same as that of the p-adic valuation space ...
Shigeki Matsutani
doaj +4 more sources
The 2-adic valuation of the general degree-2 polynomial in 2 variables [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We define the p-adic valuation tree of a polynomial f(x,y) ∈ ℤ[x,y] by which we can find its p-adic valuation at any point. This work includes diverse 2-adic valuation trees of certain degree-two polynomials in two variables.
Shubham
doaj +1 more source
Narayana sequence and the Brocard–Ramanujan equation [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let {aₙ}_{n≥0} be the Narayana sequence defined by the recurrence aₙ = aₙ₋₁ + aₙ₋₃ for all n ≥ 3 with initial values a₀ = 0 and a₁ = a₂ = 1. In this paper, we fully characterize the 3-adic valuation of aₙ + 1 and aₙ - 1, and then we find all positive ...
Mustafa Ismail +2 more
doaj +1 more source
Nontrivial lower bounds for the p-adic valuations of some type of rational numbers and an application for establishing the integrality of some rational sequences [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this note, based on a certain functional equation of the dilogarithm function, we establish nontrivial lower bounds for the p-adic valuation (where p is a given prime number) of some type of rational numbers involving harmonic numbers. Then we use our
Bakir Farhi
doaj +1 more source
Implicit linear difference equations over a non-Archi-medean ring
Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2021 Over any field an implicit linear difference equation one can reduce to the usual explicit one, which has infinitely many solutions ~ one for each initial value.
Anna Goncharuk
doaj +1 more source
Annales Mathematicae Silesianae, 2020 In [12] a close connection between stability results for the Cauchy equation and the completion of a normed space over the rationals endowed with the usual absolute value has been investigated. Here similar results are presented when the valuation of the
Schwaiger Jens
doaj +1 more source
A Unique Representation of Cyclic Codes over GR(pn,r)
Axioms, 2022 Let R be a Galois ring, GR(pn,r), of characteristic pn and of order pnr. In this article, we study cyclic codes of arbitrary length, N, over R. We use discrete Fourier transform (DFT) to determine a unique representation of cyclic codes of length, N, in ...
Sami Alabiad, Yousef Alkhamees
doaj +1 more source
Further Results on a Curious Arithmetic Function
Journal of Mathematics, 2020 Let p be an odd prime number and n be a positive integer. Let vpn, N∗, and Q+ denote the p-adic valuation of the integer n, the set of positive integers, and the set of positive rational numbers, respectively.
Long Chen, Kaimin Cheng, Tingting Wang
doaj +1 more source
On Periodic Points of the Order of Appearance in the Fibonacci Sequence
Mathematics, 2020 Let ( F n ) n ≥ 0 be the Fibonacci sequence. The order of appearance z ( n ) of an integer n ≥ 1 is defined by z ( n ) = min { k ≥ 1 : n ∣ F k } .
Eva Trojovská
doaj +1 more source
Mathematics, 2020 Let ( F n ) n ≥ 0 be the sequence of the Fibonacci numbers. The order (or rank) of appearance z ( n ) of a positive integer n is defined as the smallest positive integer m such that n divides F m .
Eva Trojovská
doaj +1 more source