Results 21 to 30 of about 2,924 (299)

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 $n$.
openaire   +2 more sources

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
doaj   +1 more source

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, Gilda Rech Bansimba, Basile Guy Richard Bossoto   +2 more
doaj   +1 more source

SOME RESULTS ON ORDERED AND UNORDERED FACTORIZATION OF A POSITIVE INTEGER [PDF]

Journal of Algebraic Systems, 2023
A well-known enumerative problem is to count the number of ways a positive integer $n$ can be factorised as $n=n_1\times n_2\times\cdots\times n_{k}$, where $n_1\geqslant n_2 \geqslant \cdots \geqslant n_{k} >1$.
Daniel Yaqubi, Madjid Mirzavaziri
doaj   +1 more source

Integer factorization as subset-sum problem

, 2022
This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer factorization to a ...
Hittmeir, Markus
core   +2 more sources

A note on solitary numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Does 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
doaj   +1 more source

On the factorization of squarefree integers [PDF]

Proceedings of the American Mathematical Society, 1952
In recent years several papers [1; 3; 4; 5; 6; 7; 9; 10; 11] have appeared dealing with the problem of "Factorisatio numerorum," the number f(n) of representations of an integer n as an ordered product of factors greater than 1. As a result, the basic combinatorial properties of f(n) and the asymptotic behavior of its summatory function are well known.
openaire   +1 more source

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, Yingyin Tao, Meng Zhang, Huaqing Li   +3 more
doaj   +1 more source

Integer factoring and compositeness witnesses [PDF]

Journal of Mathematical Cryptology, 2020
Abstract We describe a reduction of the problem of factorization of integers n ≤ x in polynomial-time (log x ) M +
Jacek Pomykala, Maciej Radziejewski
openaire   +4 more sources

On factoring of unlimited integers

Journal of Logic and Analysis, 2020
Abdelmadjid Boudaoud asked whether every unlimited integer is a sum of a limited integer and a product of two unlimited integers. Assuming Dickson's conjecture, the answer is negative.
openaire   +4 more sources