Download E-books Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics) PDF

By William Stein

It is a ebook approximately major numbers, congruences, mystery messages, and elliptic curves that you should learn hide to hide. It grew out of undergr- uate classes that the writer taught at Harvard, UC San Diego, and the college of Washington. The systematic research of quantity idea used to be initiated round 300B. C. while Euclid proved that there are in?nitely many major numbers, and in addition cleverly deduced the basic theorem of mathematics, which asserts that each optimistic integer components uniquely as a made from primes. Over one thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent quantity challenge that asks for the way to choose even if a given optimistic integer n is the world of a correct triangle, all 3 of whose aspects are rational numbers. Then one other thousand years later (in 1976), Di?e and Hellman brought the ?rst ever public-key cryptosystem, which enabled humans to speak secretely over a public communications channel without predetermined mystery; this invention and those that it revolutionized the realm of electronic communique. within the Nineteen Eighties and Nineteen Nineties, elliptic curves revolutionized quantity thought, supplying outstanding new insights into the congruent quantity challenge, primality checking out, publ- key cryptography, assaults on public-key platforms, and enjoying a valuable position in Andrew Wiles’ answer of Fermat’s final Theorem.

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