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Factorization and Primality Testing David M. Bressoud Author
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ISBN: 9780387970400

About binomial theorems I'm teeming with a lot of news, With many cheerful facts about the square on the hypotenuse. - William S. Gilbert (The Pirates of Penzance, Act I) The question of… More...

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Factorization and Primality Testing (Undergraduate Texts in Mathematics) - Bressoud, David M.
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Bressoud, David M.:

Factorization and Primality Testing (Undergraduate Texts in Mathematics) - hardcover

1989, ISBN: 9780387970400

Springer, Gebundene Ausgabe, Auflage: 1989, 254 Seiten, Publiziert: 1989-10-02T00:00:01Z, Produktgruppe: Buch, 1.2 kg, Verkaufsrang: 2543435, Ingenieurwissenschaft & Technik, Naturwissens… More...

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David M. Bressoud:
Factorization and Primality Testing - Paperback

ISBN: 9780387970400

*Factorization and Primality Testing* - Auflage 1989 / gebundene Ausgabe für 55.49 € / Aus dem Bereich: Bücher, Wissenschaft, Mathematik Medien > Bücher nein Buch (gebunden) Hardcover;Nat… More...

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David M. Bressoud:
Factorization and Primality Testing - hardcover

ISBN: 9780387970400

Hardback. New. Civilizations as separate as the Egyptians of ten thousand years ago and the Central American Mayans adopted a month of thirty days and a year of twelve months. At the oth… More...

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Bressoud, David M.:
Factorization and Primality Testing - hardcover

1989, ISBN: 0387970401

[EAN: 9780387970400], [PU: Springer Verlag], Befriedigend/Good: Durchschnittlich erhaltenes Buch bzw. Schutzumschlag mit Gebrauchsspuren, aber vollständigen Seiten. / Describes the averag… More...

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Factorization and Primality Testing David M. Bressoud Author
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9780387970400


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Details of the book - Factorization and Primality Testing David M. Bressoud Author


EAN (ISBN-13): 9780387970400
ISBN (ISBN-10): 0387970401
Hardcover
Paperback
Publishing year: 2007
Publisher: Springer New York Core >2 >T
260 Pages
Weight: 0,555 kg
Language: eng/Englisch

Book in our database since 2007-06-04T07:41:07+01:00 (London)
Detail page last modified on 2024-01-16T12:46:36+00:00 (London)
ISBN/EAN: 9780387970400

ISBN - alternate spelling:
0-387-97040-1, 978-0-387-97040-0
Alternate spelling and related search-keywords:
Book author: david bressoud, bress, gilbert william
Book title: factorization and primality testing, undergraduate text

Information from Publisher

Author: David M. Bressoud
Title: Undergraduate Texts in Mathematics; Factorization and Primality Testing
Publisher: Springer; Springer US
240 Pages
Publishing year: 1989-10-02
New York; NY; US
Language: English
57,15 € (DE)

BB; Hardcover, Softcover / Mathematik/Arithmetik, Algebra; Zahlentheorie; Verstehen; Euclidean algorithm; Mersenne prime; binomial; elliptic curve; prime number; quadratic form; Number Theory; EA; BC

1 Unique Factorization and the Euclidean Algorithm.- 1.1 A theorem of Euclid and some of its consequences.- 1.2 The Fundamental Theorem of Arithmetic.- 1.3 The Euclidean Algorithm.- 1.4 The Euclidean Algorithm in practice.- 1.5 Continued fractions, a first glance.- 1.6 Exercises.- 2 Primes and Perfect Numbers.- 2.1 The Number of Primes.- 2.2 The Sieve of Eratosthenes.- 2.3 Trial Division.- 2.4 Perfect Numbers.- 2.5 Mersenne Primes.- 2.6 Exercises.- 3 Fermat, Euler, and Pseudoprimes.- 3.1 Fermat’s Observation.- 3.2 Pseudoprimes.- 3.3 Fast Exponentiation.- 3.4 A Theorem of Euler.- 3.5 Proof of Fermat’s Observation.- 3.6 Implications for Perfect Numbers.- 3.7 Exercises.- 4 The RSA Public Key Crypto-System.- 4.1 The Basic Idea.- 4.2 An Example.- 4.3 The Chinese Remainder Theorem.- 4.4 What if the Moduli are not Relatively Prime?.- 4.5 Properties of Euler’s ø Function.- Exercises.- 5 Factorization Techniques from Fermat to Today.- 5.1 Fermat’s Algorithm.- 5.2 Kraitchik’s Improvement.- 5.3 Pollard Rho.- 5.4 Pollard p — 1.- 5.5 Some Musings.- 5.6 Exercises.- 6 Strong Pseudoprimes and Quadratic Residues.- 6.1 The Strong Pseudoprime Test.- 6.2 Refining Fermat’s Observation.- 6.3 No “Strong” Carmichael Numbers.- 6.4 Exercises.- 7 Quadratic Reciprocity.- 7.1 The Legendre Symbol.- 7.2 The Legendre symbol for small bases.- 7.3 Quadratic Reciprocity.- 7.4 The Jacobi Symbol.- 7.5 Computing the Legendre Symbol.- 7.6 Exercises.- 8 The Quadratic Sieve.- 8.1 Dixon’s Algorithm.- 8.2 Pomerance’s Improvement.- 8.3 Solving Quadratic Congruences.- 8.4 Sieving.- 8.5 Gaussian Elimination.- 8.6 Large Primes and Multiple Polynomials.- 8.7 Exercises.- 9 Primitive Roots and a Test for Primality.- 9.1 Orders and Primitive Roots.- 9.2 Properties of Primitive Roots.- 9.3Primitive Roots for Prime Moduli.- 9.4 A Test for Primality.- 9.5 More on Primality Testing.- 9.6 The Rest of Gauss’ Theorem.- 9.7 Exercises.- 10 Continued Fractions.- 10.1 Approximating the Square Root of 2.- 10.2 The Bháscara-Brouncker Algorithm.- 10.3 The Bháscara-Brouncker Algorithm Explained.- 10.4 Solutions Really Exist.- 10.5 Exercises.- 11 Continued Fractions Continued, Applications.- 11.1 CFRAC.- 11.2 Some Observations on the Bháscara-Brouncker Algorithm.- 11.3 Proofs of the Observations.- 11.4 Primality Testing with Continued Fractions.- 11.5 The Lucas-Lehmer Algorithm Explained.- 11.6 Exercises.- 12 Lucas Sequences.- 12.1 Basic Definitions.- 12.2 Divisibility Properties.- 12.3 Lucas’ Primality Test.- 12.4 Computing the V’s.- 12.5 Exercises.- 13 Groups and Elliptic Curves.- 13.1 Groups.- 13.2 A General Approach to Primality Tests.- 13.3 A General Approach to Factorization.- 13.4 Elliptic Curves.- 13.5 Elliptic Curves Modulo p.- 13.6 Exercises.- 14 Applications of Elliptic Curves.- 14.1 Computation on Elliptic Curves.- 14.2 Factorization with Elliptic Curves.- 14.3 Primality Testing.- 14.4 Quadratic Forms.- 14.5 The Power Residue Symbol.- 14.6 Exercises.- The Primes Below 5000.

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