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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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The Integer Factorization Algorithm With Pisano Period
IEEE Access, 2019 Large integer factorization is one of the basic issues in number theory and is the subject of this paper. Our research shows that the Pisano period of the product of two prime numbers (or an integer multiple of it) can be derived from the two prime ...
Liangshun Wu, H. J. Cai, Zexi Gong
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New integer factorizations [PDF]
Mathematics of Computation, 1983 New factorizations of Fibonacci numbers, Lucas numbers, and numbers of the form 2 n ± 1 {2^n} \pm 1 are presented together with the strategy (a combination of known factorization methods) used to obtain them.
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Factoring Large Integers [PDF]
Mathematics of Computation, 1974 A modification of Fermat’s difference of squares method is used for factoring large integers. This modification permits factoring n in O ( n 1 / 3 ) O({n^{1/3}}) elementary operations,
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Transfinite Lyndon words [PDF]
, 2020 In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a relaxation of the ...
Boasson, Luc, Carton, Olivier
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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 NUMBER THEORETIC FUNCTION AND ITS MEAN VALUE PROPERTY [PDF]
, 1996 Let p be a prime, n be any positive integer, a(n,p) denotes the power of p in the factorization of n!
Liu, HONGYAN, ZHANG, WENPENG
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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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Binary Codes Based on Non-Negative Matrix Factorization for Clustering and Retrieval
IEEE Access, 2020 Traditional non-negative matrix factorization methods cannot learn the subspace from the high-dimensional data space composed of binary codes. One hopes to discover a compact parts-based representation composed of binary codes, which can uncover the ...
Jiang Xiong +3 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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