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Universal exponential solution of the Yang
Universal exponential solution of the Yang

Variations on the Bloch
Variations on the Bloch

GROUP ALGEBRAS. We will associate a certain algebra to a
GROUP ALGEBRAS. We will associate a certain algebra to a

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... be the case with two-stage stochastic programs. Furthermore, the observed speed of convergence is much faster than techniques such as Benders decomposition, especially for higher dimensional problems. The paper is divided into two parts. Sections 2-6 deal exclusively with problems where the original ...
Public Key Cryptography and RSA Review: Number Theory Basics
Public Key Cryptography and RSA Review: Number Theory Basics

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fundamental concepts of algebra - Department of Mathematical

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Hensel`s treatment of primitive roots

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Contemporary Abstract Algebra (6th ed.) by Joseph Gallian

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Solutions to Midterm 1

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Category 3 (Number Theory) Packet

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The Genuine Sieve of Eratosthenes

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Lesson 6 Laws of Logarithms

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2. Basic notions of algebraic groups Now we are ready to introduce

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2. Ideals in Quadratic Number Fields

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Jumping Jiving GCD - the School of Mathematics, Applied

Efficient robust digital hyperplane fitting with bounded
Efficient robust digital hyperplane fitting with bounded

... Theorem 2 (Fonseca and Mount [6]). For a set of N points in the unit d-dimensional cube and some ε > 0, one can build a data structure with O(ε−d ) storage space, in O(N + ε−d logO(1) (ε−1 )) time, such that for a given query hyperplane H, the number of points on and bellow H can be approximately r ...
(pdf)
(pdf)

... where A and B are constants. This equation is called the Weierstrass equation for an elliptic curve. We will need to specify which field A, B, x, and y belong to, for now we will deal with R, since it is easy to visualize, but for our cryptographic applications, it will make sense to deal with finit ...
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Factorization of polynomials over finite fields

In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.The case of the factorization of univariate polynomials over a finite field, which is the subject of this article, is especially important, because all the algorithms (including the case of multivariate polynomials over the rational numbers), which are sufficiently efficient to be implemented, reduce the problem to this case (see Polynomial factorization). It is also interesting for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory.As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.
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