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Factoring, finding a non-trivial factorization of a composite positive integer, is believed to be a hard problem. How hard we think it is, however, changes almost on a daily basis. Predicting how hard factoring will be in the future, an important issue for cryptographic applications of composite numbers, is therefore a challenging task.
Lenstra, Arjen K.
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In the context of globalization, the transactions between business partners become more and more diverse and require special attention from commercial banks and factoring companies, both with regard to settlement, in order to avoid possible financial ...
Delia DAVID +3 more
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Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which is inspired by the Hindley-Rosen technique for confluence.
Accattoli, Beniamino +2 more
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A method of factoring and the factorization of 𝐹₇ [PDF]
The continued fraction method for factoring integers, which was introduced by D. H. Lehmer and R. E. Powers, is discussed along with its computer implementation. The power of the method is demonstrated by the factorization of the seventh Fermat number
Morrison, Michael A., Brillhart, John
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A one line factoring algorithm [PDF]
We describe a variant of Fermat’s factoring algorithm which is competitive with SQUFOF in practice but has heuristic run time complexity O(n1/3) as a general factoring algorithm.
William B. Hart, Hart, William B.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Golnaz Badkobeh +7 more
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Practical polynomial factoring in polynomial time [PDF]
State of the art factoring in Q[x] is dominated in theory by a combinatorial reconstruction problem while, excluding some rare polynomials, performance tends to be dominated by Hensel lifting.
Andrew Novocin +7 more
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Complete-factors and f-factors
Let \(G\) be a graph and \(F\) a spanning subgraph of \(G\) with at least two components and with all components complete. Let \(f\) be an integer-valued function defined on \(V(G)\) with \(\sum_{x \in V(G)} f(x)\) even. If for each component \(C\) of \(F\), \(G - V(C)\) has an \(f\)-factor (that is, a spanning subgraph \(H\) in which \(\deg_H(x) = f(x)
Hikoe Enomoto, Taro Tokuda
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RESUMENEl artículo presenta, una conceptualización general de lo que es el factoring, el origen del mismo, su evolución y hace una clasificación de los distintos tipos de factoring.
Rosenthal, Alberto
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The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the matrix and its adjoint are available or the entries of the matrix can be sampled individually.
Yingzhou Li +4 more
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