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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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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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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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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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On the factorization of consecutive integers [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2009 A classical result of Sylvester [21] (see also [16], [17]), generalizing Bertrand’s Postulate, states that the greatest prime divisor of a product of k consecutive integers greater than k exceeds k. More recent work in this vein, well surveyed in [18], has focussed on sharpening Sylvester’s theorem, or upon providing lower bounds for the number of ...
Michael Filaseta +2 more
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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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On the Number of Factorizations of an Integer [PDF]
Integers, 2011 AbstractLet ƒ(
Florian Luca +1 more
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A babystep-giantstep method for faster deterministic integer factorization [PDF]
Mathematics of Computation, 2016 In 1977, Strassen presented a deterministic and rigorous algorithm for solving the problem of computing the prime factorization of natural numbers $N$. His method is based on fast polynomial arithmetic techniques and runs in time $\widetilde{O}(N^{1/4})$,
Markus Hittmeir
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The factor-difference set of integers [PDF]
Acta Arithmetica, 1997 The set \(D(n) = \{d:\;d=| a-b| ,\;n=ab\} = \{d_0 < d_1 < \cdots 0\) there are \(k\) distinct integers \(N_1 < N_2 < \cdots
Paul Erdős, Moshe Rosenfeld
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Localized factorizations of integers [PDF]
Proceedings of the London Mathematical Society, 2010 34 pages. Added reference [10] to a paper of Nair and Tenenbaum which contains a result similar to Lemma 2.2 and which appeared prior to the publication of this paper. Simplified the proof of Lemma 2.2 using ideas from [10]. Removed part (a) of Lemma 2.2, as it is now redundant.
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