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 that you should learn conceal 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 examine of quantity conception was once initiated round 300B. C. whilst Euclid proved that there are in?nitely many leading numbers, and in addition cleverly deduced the basic theorem of mathematics, which asserts that each optimistic 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 the way to make a decision even if a given optimistic 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 communique. within the Eighties and Nineties, elliptic curves revolutionized quantity concept, supplying remarkable new insights into the congruent quantity challenge, primality trying out, publ- key cryptography, assaults on public-key structures, and enjoying a valuable function in Andrew Wiles’ solution of Fermat’s final Theorem.

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