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

By William Stein

This can be a publication approximately top numbers, congruences, mystery messages, and elliptic curves so that you can learn disguise to hide. It grew out of undergr- uate classes that the writer taught at Harvard, UC San Diego, and the collage of Washington. The systematic learn of quantity thought used to be initiated round 300B. C. whilst Euclid proved that there are in?nitely many major numbers, and in addition cleverly deduced the basic theorem of mathematics, which asserts that each confident integer elements uniquely as a manufactured from primes. Over one thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent quantity challenge that asks for how to determine even if a given confident integer n is the world of a correct triangle, all 3 of whose facets 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 conversation. within the Eighties and Nineties, elliptic curves revolutionized quantity idea, offering remarkable new insights into the congruent quantity challenge, primality trying out, publ- key cryptography, assaults on public-key structures, and taking part in a imperative position in Andrew Wiles’ answer of Fermat’s final Theorem.

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