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Chapters: Finite Fields, Modular Arithmetic, Cyclic Redundancy Check, Euler's Totient Function, Fermat's Little Theorem, Chinese Remainder Theorem, Euler's Theorem, Elliptic Curve Cryptography, Carmichael Number, Linear Congruence Theorem, Congruence Relation, Proofs of Fermat's Little Theorem, Linear Congruential Generator, Quadratic Reciprocity, Legendre Symbol, Bch Code, Lenstra Elliptic Curve Factorization, Fermat Primality Test, Nimber, Euler's Criterion, Jacobi Symbol, Weil Conjectures, Computation of Crc, Quadratic Residue, Quartic Reciprocity, Cubic Reciprocity, Schoof's Algorithm, Trigonometry in Galois Fields, Mathematics of Crc, Primitive Root Modulo N, Gauss's Lemma, Modular Representation Theory, Miller-rabin Primality Test, Finite Field Arithmetic, Hidden Field Equations, Aks Primality Test, Multiplicative Group of Integers Modulo N, Network Coding, Montgomery Reduction, Verhoeff Algorithm, Luhn Algorithm, Cipolla's Algorithm, Modular Exponentiation, Drinfel'd Module, Tonelli-shanks Algorithm, Frobenius Endomorphism, Wilson's Theorem, Solovay-strassen Primality Test, Zeller's Congruence, Sato-tate Conjecture, Luhn Mod N Algorithm, Linear Code, Hensel's Lemma, Diffie-hellman Problem, Dowling Geometry, Kochanski Multiplication, Discrete Logarithm, Galois/counter Mode, Rijndael S-Box, Cantor-zassenhaus Algorithm, Local Zeta-Function, Berlekamp's Algorithm, Pocklington's Algorithm, Modular Multiplicative Inverse, Table of Costs of Operations in Elliptic Curves, Hasse-witt Matrix, Carmichael Function, Goppa Code, Cyclic Code, Residue Number System, Cmac, Chevalley-warning Theorem, Zech's Logarithms, Rijndael Mix Columns, Additive Polynomial, Park-miller Random Number Generator, Ternary Golay Code, Chien Search, Beaver Bit-Vector Decision Procedure, Mod N Cryptanalysis, Schoof-elkies-atkin Algorithm, Congruence of Squares, Multiplicative Order, Vedic Square, Multi-S01, Steinberg Representation, Gf(2), Method of Succes...More: http://booksllc.net/?id=25272 ... Read more

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In number theory, Fermat's Last Theoremstates that no three positive integers a , b , and ccan satisfy the equation an+ bn= cnfor any integer value of ngreater than two. This theorem was first conjectured by Pierre de Fermat in 1637, but was not proven until 1995 despite the efforts of many illustrious mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the ? modularity theorem in the 20th. It is among the most famous theorems in the ? history of mathematics. Fermat left no proof of the conjecture for all n , but he did prove the special case n= 4. This reduced the problem to proving the theorem for exponents nthat are odd prime numbers. Over the next two centuries (1637? 1839), the conjecture was proven for only the primes 3, 5, and 7, although ? Sophie Germain proved a special case for all primes less than 100. In the mid-19th century, Ernst Kummer proved the theorem for a large (probably infinite) class of primes known as regular primes. ... Read more

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High Quality Content by WIKIPEDIA articles! A pseudoprime is a probable prime (an integer which shares a property common to all prime numbers) which is not actually prime. Pseudoprimes can be classified according to which property they satisfy.The most important class of pseudoprimes come from Fermat's little theorem and hence are called Fermat pseudoprimes. This theorem states that if p is prime and a is coprime to p, then ap?1 ? 1 is divisible by p. If a number x is not prime, a > 1 is coprime to x and x divides ax?1 ? 1, then x is called a pseudoprime to base a. Some sources use variations of this definition, for example to only allow odd numbers to be pseudoprimes.A number x that is a pseudoprime for all values of a that are coprime to x is called a Carmichael number. ... Read more

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This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more

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Some short proofs of Fermat1s last theorem by the inventorof Hal Algebra and Hal TreesThis is an application of Hal Algebra.. ... Read more

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This is nonfiction commentary. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Trick or Treatment, Big Bang, the Code Book, Fermat's Last Theorem. Source: Wikipedia. Free updates online. Not illustrated. Excerpt: Trick or Treatment? Alternative Medicine on Trial (North American title: Trick or Treatment: The Undeniable Facts about Alternative Medicine) is a 2008 book about alternative medicine by Simon Singh and Edzard Ernst. Singh is a physicist and the writer of several popular science books. Ernst is a professor of complementary medicine. The book evaluates the scientific evidence for acupuncture, homeopathy, herbal medicine, and chiropractic, and briefly covers 36 other treatments. It finds that the scientific evidence for these alternative treatments is generally lacking. Homeopathy is concluded to be completely ineffective: "It's nothing but a placebo, despite what homeopaths say". Although the book presents evidence that acupuncture, chiropractic and herbal remedies have limited efficacy for certain ailments, the authors conclude that the dangers of these treatments outweigh any potential benefits. Such potential risks outlined by the authors are contamination or unexpected interactions between components in the case of herbal medicine, risk of infection in the case of acupuncture and the potential for chiropractic manipulation of the neck to cause delayed stroke. The book is very critical of Prince Charles' advocacy of alternative medicine and the actions of his now-defunct Foundation for Integrated Health. The book is dedicated, in an ironic fashion, to the Prince. The book received generally good reviews. The New England Journal of Medicine reviewed the book and said this about the authors: "Simon Singh is a physicist and science journalist, and his coauthor, Edzard Ernst, is a physician and professor of complement...More: http://booksllc.net/?id=21193032 ... Read more

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This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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This digital document is an article from Science and Its Times, brought to you by Gale®, a part of Cengage Learning, a world leader in e-research and educational publishing for libraries, schools and businesses.The length of the article is 747 words.The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase.You can view it with any web browser.The histories of science, technology, and mathematics merge with the study of humanities and social science in this interdisciplinary reference work. Essays on people, theories, discoveries, and concepts are combined with overviews, bibliographies of primary documents, and chronological elements to offer students a fascinating way to understand the impact of science on the course of human history and how science affects everyday life. Entries represent people and developments throughout the world, from about 2000 B.C. through the end of the twentieth century. ... Read more

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High Quality Content by WIKIPEDIA articles! The Fermat polygonal number theorem states that every positive integer is a sum of at most n n-gonal numbers. That is, every positive number can be written as the sum of three or fewer triangular numbers, and as the sum of four or fewer square numbers, and as the sum of five or fewer pentagonal numbers, and so on. Joseph Louis Lagrange proved the square case in 1770 and Gauss proved the triangular case in 1796, but the theorem was not resolved until it was finally proven by Cauchy in 1813. For odd positive integers a and b such that b2 < 4a and 3a < b2 + 2b + 4 we can find nonnegative integers s,t,u and v such that a = s2 + t2 + u2 + v2 and b = s + t + u + v. ... Read more

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31 pages, small trade-size paperback math book ... Read more