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On the greatest and least prime factors of n! + 1
On the greatest and least prime factors of n! + 1

Towards Fully Automated Axiom Extraction for Finite-Valued Logics
Towards Fully Automated Axiom Extraction for Finite-Valued Logics

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Part VIII Elliptic curves cryptography and factorization

STRATIFICATION BY THE LOCAL HILBERT
STRATIFICATION BY THE LOCAL HILBERT

... the strata where the invariant is maximal. In Hironaka’s work this invariant is the Hilbert-Samuel function. Thus it needs the determination of the strata of maximality of the local Hilbert-Samuel function. However, to our knowledge, there does not exist an algorithm for this step that works in any ...
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... – Example: Alice chooses x, x’ {0,1}n if x’= 0n set y=x o.w. set y=f(x) – The protocol is still secure, but with probability 1/2n not complete – The resulting function f(x,x’) is easy to invert: • given y {0,1}n set inverse as (y, 0n ) ...
Fixed points of polynomial maps. I. Rotation subsets of the circles
Fixed points of polynomial maps. I. Rotation subsets of the circles

Introductory notes on the model theory of valued fields
Introductory notes on the model theory of valued fields

x + 1 - mrhubbard
x + 1 - mrhubbard

... The first step in factoring is to determine its greatest monomial factor. If there is a greatest monomial factor other than 1, use the distributive property to rewrite the given polynomial as the product of this greatest monomial factor and a polynomial. Example 1 Factor each polynomial. ...
A KRYLOV METHOD FOR THE DELAY EIGENVALUE PROBLEM 1
A KRYLOV METHOD FOR THE DELAY EIGENVALUE PROBLEM 1

Classification of Finite Rings of Order p2
Classification of Finite Rings of Order p2

允許學生個人、非營利性的圖書館或公立學校合理使用 本
允許學生個人、非營利性的圖書館或公立學校合理使用 本

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... represent numbers, we can express the numerical values and relationship of numerical values succinctly. In the above examples, we obtain many expressions involving letters, namely ab, a+b, 40r, vt … etc. Expressions with numbers and letters linked up by mathematical operations are called Algebraic ...
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Video Based Head Detection and Tracking Surveillance System
Video Based Head Detection and Tracking Surveillance System

... on histogram of gradients (HoG) feature[5]. Simultaneously, motion and appearance information are extracted from the video sequence. Based Bayesian theory, we use two likelihood to evaluate the probability of a detected region represents an actual human head. The false positives are eliminated and t ...
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A Note on Locally Nilpotent Derivations and Variables of k[X,Y,Z]

Averaging sums of powers of integers and Faulhaber polynomials
Averaging sums of powers of integers and Faulhaber polynomials

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Mr. Sims - Algebra House

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Galois Groups and Fundamental Groups

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... Privacy with Static Optimality Algorithm: – Start with random weights ri in range [1,c] – At any point in time wi = ri + ci Run with private • ci is # of times element ai was requested. counter – Arrange elements according to weights – Privacy: from privacy of counters • list depends on counters pl ...
Algebraic Topology
Algebraic Topology

... 8. Show that for X = RP2 the previous exercise is false when F is replaced by Z. (There is a pairing: it does not give rise to an isomorphism.) 9. For π a group, define Hi(π) to be Hi(K(π,1)). Prove a Mayer-Vietoris sequence for amalgamated free products, where the subgroup injects. 10. Show that t ...
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Math 3121 Abstract Algebra I

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256 Bit Key — Is It Big Enough?

http://www.math.uni-muenster.de/u/lueck/publ/lueck/surveyclassi04.pdf
http://www.math.uni-muenster.de/u/lueck/publ/lueck/surveyclassi04.pdf

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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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