Results 41 to 50 of about 41,624 (236)
A Paradigmatic Approach to Find Equal Sum Partitions of Zero-Divisors via Complete Graphs
Journal of Chemistry, 2022 In computer science and mathematics, a partition of a set into two or more disjoint subsets with equal sums is a well-known NP-complete problem. This is a hard problem and referred to as the partition problem or number partitioning.
M. Haris Mateen +4 more
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Two divisors of (n^2+1)/2 summing up to {\delta}n+{\epsilon}, for {\delta} and {\epsilon} even [PDF]
, 2014 In this paper we are dealing with the problem of the existence of two divisors of $(n^2+1)/2$ whose sum is equal to $\delta n+\varepsilon$, in the case when $\delta$ and $\varepsilon$ are even, or more precisely in the case in which $\delta\equiv ...
Bujačić, Sanda
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Sums of fractional parts and sum of restricted divisors of a number
Gulf Journal of Mathematics, 2021 Let us consider a strictly increasing sequence of positive integers an such that A(x) is the distribution function of the sequence. That is, A(x)=∑ an≤ x 1. We study the sum ∑ an≤ x ans{x / an} and apply this formula in the study of the sum of a-divisors
R. Jakimczuk
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A note on generalized Zumkeller numbers [PDF]
Notes on Number Theory and Discrete MathematicsA positive integer n is called an e-Zumkeller number if the exponential divisors of n can be partitioned into two disjoint subsets of equal sum. Generalizing the concept of e-Zumkeller numbers, we define multiplicatively e-Zumkeller numbers. In addition,
Jayanta Kalita, Helen K. Saikia
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An analogue in certain unique factorization domains of the Euclid-Euler theorem on perfect numbers
International Journal of Mathematics and Mathematical Sciences, 1990 We show that there exists a natural extention of the sum of divisors function to all unique factorization domains F having a finite number of units such that if a perfect number in F is defined to be an integer η whose proper divisors sum to η, then the ...
Wayne L. McDaniel
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Sums of Numbers with Many Divisors
Journal of Number Theory, 1999 For a fixed integer \(k\geq 2\), there is the interesting problem of representing \(n\) as \(m_1+\cdots+m_k\), with each \(m_i\) having, in some sense, many divisors. The divisor function \(d(n)\) has a maximum size which is essentially \(D(n)=\exp(\log 2\log n/\log\log n)\), and one may interpret the problem by prescribing the condition that \(d(m_i ...
Erdős, Paul, Montgomery, Hugh L
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Arithmetic functions associated with infinitary divisors of an integer
International Journal of Mathematics and Mathematical Sciences, 1993 The infinitary divisors of a natural number n are the products of its divisors of the form pyα2α, where py is a prime-power component of n and ∑αyα2α (where yα=0 or 1) is the binary representation of y.
Graeme L. Cohen, Peter Hagis
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A study of the total graph in genetic code algebra [PDF]
Network Biology, 2022 Suppose R be a commutative ring and Z(R) its set of zero-divisors. Total graph is the (undirected) graph where set of all elements of R is taken as the vertex set and two vertices say x and y (x not equals to y) in R are adjacent if and only if their sum
Birinchi Kumar Boruah, Tazid Ali
doaj
N $$ \mathcal{N} $$ = 2* Schur indices
Journal of High Energy Physics, 2023 We find closed-form expressions for the Schur indices of 4d N $$ \mathcal{N} $$ = 2* super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with
Yasuyuki Hatsuda, Tadashi Okazaki
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A survey of the alternating sum-of-divisors function [PDF]
, 2011 We survey arithmetic and asymptotic properties of the alternating sum-of-divisors function β defined by β(pa) = pa − pa−1 + pa−2 − · · · + (−1)a for every prime power pa (a ≥ 1), and extended by multiplicativity. Certain open problems are also stated.
L. Tóth
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