Introductory Number Theory
نویسنده
چکیده
We will start with introducing congruences and investigating modular arithmetic: the set Z/nZ of “integers modulo n” forms a ring. This ring is a field if and only if n is a prime number. A study of the multiplicative structure leads to Fermat’s Little Theorem (for prime n) and to the Euler phi function and Euler’s generalization of Fermat’s Theorem. Another basic tool is the Chinese Remainder Theorem. Building on this basis, we will have a look at modern cryptographic systems. Then we will get back to more classical number theory and deal with quadratic residues and the famous quadratic reciprocity law that was discovered and proved (several times!) by Gauss. This leads naturally to the study of solutions to equations like a X + b Y 2 = c Z
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تاریخ انتشار 2007