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The Fundamentals: Algorithms, the Integers, and Matrices
The Fundamentals: Algorithms, the Integers, and Matrices

Module - Algebraic Fractions
Module - Algebraic Fractions

Fractions - 3P Learning
Fractions - 3P Learning

Continued Fractions and Approximations
Continued Fractions and Approximations

Lecture 5 The Euclidean Algorithm
Lecture 5 The Euclidean Algorithm

14(4)
14(4)

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... Remarks: (1), (2), (3) are well-known properties of Dedekind sums. (See [1], p. 62.) (4) through (8) are well-known properties of linear recurrences of order 2. (See [2], p. 193-194). (9) can be proved via (6) or by induction on n. THE MAIN RESULTS Theorem 1: Let {un } be a linear recurrence of orde ...
36(3)
36(3)

Coloring Signed Graphs
Coloring Signed Graphs

Harvard-MIT Mathematics Tournament
Harvard-MIT Mathematics Tournament

Elementary Number Theory: Primes, Congruences
Elementary Number Theory: Primes, Congruences

16(4)
16(4)

... Over the years, much use has been made of Pascal's triangle, part of which is shown in Table 1.1. The original intention was to read the table horizontally, when its nth row gives, in order, the coefficients of xm {m = 0, 1, ..., n) for the binomial expansion of (1 + x)n . Pargeter [1] pointed out t ...
Local  - cosec
Local - cosec

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Full text

Lectures on Number Theory
Lectures on Number Theory

Simultaneous Approximation and Algebraic Independence
Simultaneous Approximation and Algebraic Independence

a, b
a, b

Number Theory - Redbrick DCU
Number Theory - Redbrick DCU

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HI.:jTOR Y OF HINDU MATHEMATICS

Number Theory - Redbrick DCU
Number Theory - Redbrick DCU

Math III_ Midterm Review 2013 Answer Section
Math III_ Midterm Review 2013 Answer Section

... What is the relative maximum and minimum of the function? ____ 34. a. The relative maximum is at (–1.53, 8.3) and the relative minimum is at (1.2, –12.01). b. The relative maximum is at (–1.53, 12.01) and the relative minimum is at (1.2, –8.3). c. The relative maximum is at (–1.2, 8.3) and the rela ...
Lower bound theorems for general polytopes
Lower bound theorems for general polytopes

p-ADIC QUOTIENT SETS
p-ADIC QUOTIENT SETS

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HOSCCFractions_G3_G4_G5_SS_11 12 13

Fractions and Decimals
Fractions and Decimals

< 1 2 3 4 5 6 7 8 9 10 ... 164 >

Vincent's theorem

In mathematics, Vincent's theorem—named after Alexandre Joseph Hidulphe Vincent—is a theorem that isolates the real roots of polynomials with rational coefficients.Even though Vincent's theorem is the basis of the fastest method for the isolation of the real roots of polynomials, it was almost totally forgotten, having been overshadowed by Sturm's theorem; consequently, it does not appear in any of the classical books on the theory of equations (of the 20th century), except for Uspensky's book. Two variants of this theorem are presented, along with several (continued fractions and bisection) real root isolation methods derived from them.
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