Results 1 to 10 of about 163 (134)

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   +3 more sources

Overpartitions in terms of 2-adic valuation

Aequationes Mathematicae
Abstract In this paper, we consider the 2-adic valuation of integers and provide an alternative representation for the generating function of the number of overpartitions of an integer. As a consequence of this result, we obtain a new formula and a new combinatorial interpretation for the number of overpartitions of an integer.
Mircea Merca, Merca Mircea
exaly   +3 more sources

The 2-adic valuation of a sequence arising from a rational integral

Journal of Combinatorial Theory - Series A, 2008
We analyze properties of the 2-adic valuations of an integer sequence that originates from an explicit evaluation of a quartic integral. We also give a combinatorial interpretation of the valuations of this sequence. Connections with the orbits arising from the Collatz (3x+1) problem are discussed.
Tewodros Amdeberhan, VÍCTOR H Moll
exaly   +3 more sources

Euler’s partition function in terms of 2-adic valuation

Boletin De La Sociedad Matematica Mexicana
AbstractThe 2-adic valuation of an integer n is the exponent of the highest power of 2 that divides n and is denoted by $$\nu _2(n)$$ ν 2 ( n )
Mircea Merca, Merca Mircea
exaly   +2 more sources

The2-adic and3-adic valuation of the Tripell sequence and an application

Turkish Journal of Mathematics, 2020
Summary: Let \((T_n)_{n\ge 0}\) denote the Tripell sequence, defined by the linear recurrence \(T_n=2T_{n-1}+T_{n-2}+T_{n-3}\) for \(n\ge 3\) with \(T_0=0\), \(T_1=1\) and \(T_2=2\) as initial conditions. In this paper, we study the 2-adic and 3-adic valuation of the Tripell sequence and, as an application, we determine all Tripell numbers which are ...
Jhon J Bravo, JOSÉ L Ramirez
exaly   +3 more sources

SOLVING QUADRATIC AND CUBIC DIOPHANTINE EQUATIONS USING 2-ADIC VALUATION TREES

Rocky Mountain Journal of Mathematics
18 pages, 10 figures, 3 ...
Eva G Goedhart, Bianca Thompson
exaly   +3 more sources

On Fibonacci Numbers of Order r Which Are Expressible as Sum of Consecutive Factorial Numbers

Mathematics, 2021
Let (tn(r))n≥0 be the sequence of the generalized Fibonacci number of order r, which is defined by the recurrence tn(r)=tn−1(r)+⋯+tn−r(r) for n≥r, with initial values t0(r)=0 and ti(r)=1, for all 1≤i≤r.
Eva Trojovská , Pavel Trojovský
doaj   +1 more source

The 2-adic Valuation of Stirling Numbers [PDF]

Experimental Mathematics, 2008
21 ...
Amdeberhan, Tewodros, Manna, Dante, Moll, Victor H.   +2 more
openaire   +3 more sources

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

THE 2-ADIC VALUATIONS OF STIRLING NUMBERS OF THE SECOND KIND [PDF]

International Journal of Number Theory, 2012
In this paper, we investigate the 2-adic valuations of the Stirling numbers S(n, k) of the second kind. We show that v2(S(4i, 5)) = v2(S(4i + 3, 5)) if and only if i ≢ 7 (mod 32). This confirms a conjecture of Amdeberhan, Manna and Moll raised in 2008. We show also that v2(S(2n+ 1, k + 1)) = s2(n) - 1 for any positive integer n, where s2(n) is the sum ...
Hong, Shaofang, Zhao, Jianrong, Zhao, Wei   +2 more
openaire   +2 more sources