Results 11 to 20 of about 391,497 (318)
Labeled Factorization of Integers [PDF]
The Electronic Journal of Combinatorics, 2009 The labeled factorizations of a positive integer $n$ are obtained as a completion of the set of ordered factorizations of $n$. This follows a new technique for generating ordered factorizations found by extending a method for unordered factorizations that relies on partitioning the multiset of prime factors of $n$.
Augustine O. Munagi
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A novel approach to explore common prime divisor graphs and their degree based topological descriptor. [PDF]
PLoS ONEFor the construction of a common prime divisor graph, we consider an integer [Formula: see text] with its prime factorization, where [Formula: see text] are distinct primes and [Formula: see text] are fixed positive integers. Every divisor of the integer
Ali N A Koam +3 more
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Pseudoprime factorizations of integer matrices
Linear Algebra and its Applications, 2008 AbstractWe give a method of factoring integer matrices in Zn×n into components such that the factorization is not unique unless certain information is known. In Section 2, we introduce this method of factorization and provide theorems which establish its well-definedness.
Dorothy Wallace, Walker White
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Faster deterministic integer factorization [PDF]
Mathematics of Computation, 2012 The best known unconditional deterministic complexity bound for computing the prime factorization of an integer N is O(M_int(N^(1/4) log N)), where M_int(k) denotes the cost of multiplying k-bit integers. This result is due to Bostan--Gaudry--Schost, following the Pollard--Strassen approach.
Edgar Costa, David J. Harvey
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New types of finite groups and generated algorithm to determine the integer factorization by Excel
, 2020 M. M. Torki, S. Khalil
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On the number of factorizations of an integer
, 2016 Let $f(n)$ denote the number of unordered factorizations of a positive integer $n$ into factors larger than $1$. We show that the number of distinct values of $f(n)$, less than or equal to $x$, is at most $\exp \left( C \sqrt{\frac{\log x}{\log \log x}} \left( 1 + o(1) \right) \right)$, where $C=2 \sqrt{2/3}$ and $x$ is sufficiently large.
R. Balasubramanian, Priyamvad Srivastav
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Rydberg-atom experiment for the integer factorization problem [PDF]
Physical Review Research, 2023 The task of factoring integers poses a significant challenge in modern cryptography, and quantum computing holds the potential to efficiently address this problem compared to classical algorithms.
Juyoung Park +8 more
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Integer Factorization with Compositional Distributed Representations [PDF]
Neuro Inspired Computational Elements Workshop, 2022 In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural networks and ...
D. Kleyko +7 more
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Some factorization results on polynomials having integer coefficients [PDF]
Communications in Algebra, 2023 In this article, we prove some factorization results for several classes of polynomials having integer coefficients, which in particular yield several classes of irreducible polynomials.
Jitender Singh, Rishu Garg
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Remark on Laquer's theorem for circulant determinants [PDF]
International Journal of Group Theory, 2023 Olga Taussky-Todd suggested the problem of determining the possible values of integer circulant determinants. To solve a special case of the problem, Laquer gave a factorization of circulant determinants. In this paper, we give a modest generalization of
Naoya Yamaguchi, Yuka Yamaguchi
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