Elementary Number Theory: Primes, Congru

Elementary Number Theory: Primes, Congru
Pris
Pris
439,- 439,-
E-Bok
Format E-Bok
Kopisperre Teknisk DRM
Filformat PDF
Utgivelsesår 2008
Forlag Springer New York
Språk Engelsk
ISBN 9780387855257
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Innbundet Engelsk

Om Elementary Number Theory: Primes

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predetermined secret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public- key systems, and playing a central role in Andrew Wiles' resolution of Fermat's Last Theorem.


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