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 e-book approximately best numbers, congruences, mystery messages, and elliptic curves so you might learn disguise 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 conception was once initiated round 300B. C. whilst Euclid proved that there are in?nitely many best numbers, and likewise cleverly deduced the basic theorem of mathematics, which asserts that each optimistic integer components uniquely as a made of primes. Over one thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent quantity challenge that asks for how to make your mind up 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 area of electronic verbal exchange. within the Nineteen Eighties and Nineties, elliptic curves revolutionized quantity idea, supplying impressive new insights into the congruent quantity challenge, primality checking out, publ- key cryptography, assaults on public-key structures, and taking part in a important function in Andrew Wiles’ solution of Fermat’s final Theorem.

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