Elementary Number Theory: Primes, Congruences, and Secrets / Stein, William
Tác giả : Stein, William
Nhà xuất bản : Springer
Năm xuất bản : 2009
Mô tả vật lý : 173 p.
Số phân loại : 512.7
Chủ đề : 1. Mathematics ; Number theory ; Curves, Elliptic. 2. Book.
Thông tin chi tiết
Tóm tắt : | The systematic study of number theory was initiated around 300B.C. when Euclid proved that there are infinitely many prime numbers. At the same time, he also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over 1000 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 1000 years later (in 1976), Diffie and Hellman introduced the first ever public-key cryptosystem, which enabled two people to communicate secretly 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, public-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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https://repository.vnu.edu.vn/handle/VNU_123/30757 |