相关论文: Note on Integer Factoring Methods I

This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion uses a single linear differential form defined from the…

Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods…

A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for the evaluation of Feynman diagrams. The operational rules are described and the method is…

By establishing an interesting connection between ordinary Bell polynomials and rational convolution powers, some composition and inverse relations of Bell polynomials as well as explicit expressions for convolution roots of sequences are…

Let $\{u_{n}\}_{n \geq 0}$ be a non-degenerate binary recurrence sequence with positive discriminant. In this paper, we consider the Diophantine equation $u_m + u_n = a_1 n_1! + \cdots + a_k n_k!$ and prove that there are only finitely many…

The method of obtaining the set of noncanonical hypercomplex number systems by conversion of infinite hypercomplex number system to finite hypercomplex number system depending on multiplication rules and factorization method is described.…

We propose a rather elementary method to compute a certain family of integrals on the half line, depending on the integer parameters $n\geq q\geq 1$.

In this paper, we will describe a new factorization algorithm based on the continuous representation of Gauss sums, generalizable to orders j>2. Such an algorithm allows one, for the first time, to find all the factors of a number N in a…

These notes present an approach to obtaining the basic operations of addition and multiplication on the natural numbers in terms of elementary results about commutative monoids.

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

We introduce a new factorial function which agrees with the usual Euler gamma function at both the positive integers and at all half-integers, but which is also entire. We describe the basic features of this function.

Set out here are some fundamental theories that may be regarded as newly discovered metamathematics of the odd integers in relation to the Collatz conjecture (also called the 3x+1 problem). Originally motivated by the requirement to invent…

In this article we establish two new results on quantitative Diophantine approximation for one-parameter families of diagonal ternary indefinite forms. In the first result, we consider quadratic forms taking values at prime points. In the…

A kind of spatial fractional diffusion equations in this paper are studied. Firstly, an L1 formula is employed for the spatial discretization of the equations. Then, a second order scheme is derived based on the resulting semi-discrete…

A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.

The aim of this paper is to introduce a new Newton-type iterative method and then to show that this process converges to the unique solution of the scalar nonlinear equation f(x)=0 under weaker conditions involving only f and f' by fixed…

We study the arithmetical structures on the complete graph $K_9$. Our method is based on studying the solutions to writing the unit as a sum of 9 unit fractions. We work from the perspective of the Diophantine equation and use some…

Diophantine equations are multivariate equations, usually polynomial, in which only integer solutions are admitted. A brute force method for finding solutions would be to systematically substitute possible integer solutions and check for…

Nonnegative Matrix Factorization (NMF) is a widely used technique for data representation. Inspired by the expressive power of deep learning, several NMF variants equipped with deep architectures have been proposed. However, these methods…

This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…