Results 11 to 20 of about 249,312 (242)
A generalization of the ABS algorithms and its application to some special real and integer matrix factorizations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 In 1984, Abaffy, Broyden, and Spediacto (ABS) introduced a class of the so-called ABS algorithms to solve systems of real linear equations. Later, the scaled ABS, the extended ABS, the block ABS, and the integer ABS algorithms were introduced leading to ...
E. Golpar Raboky, N. Mahdavi-Amiri
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Integer factorization with a neuromorphic sieve [PDF]
2017 IEEE International Symposium on Circuits and Systems (ISCAS), 2017 The bound to factor large integers is dominated by the computational effort to discover numbers that are smooth, typically performed by sieving a polynomial sequence. On a von Neumann architecture, sieving has log-log amortized time complexity to check each value for smoothness.
John V. Monaco, Manuel M. Vindiola
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Scheme of extending elliptic curve method to three phases
网络与信息安全学报, 2018 Elliptic curve method for integer factorization (ECM) is one of the most popular integer factorization algorithms,and it was firstly proposed by Lenstra in 1985.The original ECM contained just first phase.Since its invention,researches about the ...
Guiwen LUO
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Designs, Codes and Cryptography, 2000 The purpose of this survey is to describe how modern factoring algorithms work.
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On the factorization of integrers [PDF]
Proceedings of the American Mathematical Society, 1970 The order of magnitude of the average of the exponents in the canonical factorization of an integer is discussed. In particular, it is shown that this average has normal order one and a result which implies that the average order is one is also derived.
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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 $n$.
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Integer Factorization – Cryptology Meets Number Theory
Scientific Journal of Gdynia Maritime University, 2019 Integer factorization is one of the oldest mathematical problems. Initially, the interest in factorization was motivated by curiosity about behaviour of prime numbers, which are the basic building blocks of all other integers.
Josef Pieprzyk
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Integer Factorization with Compositional Distributed Representations
, 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 ...
Olshausen, Bruno A. +21 more
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Lattice Points on the Fermat Factorization Method
Journal of Mathematics, 2022 In this paper, we study algebraic properties of lattice points of the arc on the conics x2−dy2=N especially for d=1, which is the Fermat factorization equation that is the main idea of many important factorization methods like the quadratic field sieve ...
Regis Freguin Babindamana +2 more
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A note on solitary numbers [PDF]
Notes on Number Theory and Discrete MathematicsDoes 14 have a friend? Until now, this has been an open question. In this note, we prove that a potential friend F of 14 is an odd, non-square positive integer.
Sagar Mandal
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