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 major 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 research of quantity conception used to be initiated round 300B. C. whilst Euclid proved that there are in?nitely many top numbers, and in addition cleverly deduced the elemental theorem of mathematics, which asserts that each confident integer elements uniquely as a manufactured from primes. Over 1000 years later (around 972A. D. ) Arab mathematicians formulated the congruent quantity challenge that asks for how to determine 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 area of electronic conversation. within the Nineteen Eighties and Nineties, elliptic curves revolutionized quantity thought, offering impressive new insights into the congruent quantity challenge, primality trying out, publ- key cryptography, assaults on public-key structures, and taking part in a vital function in Andrew Wiles’ answer of Fermat’s final Theorem.

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