Fundamental Number Theory with ApplicationsCRC Press, 1997年9月10日 - 464 頁 Beginning with the arithmetic of the rational integers and proceeding to an introduction of algebraic number theory via quadratic orders, Fundamental Number Theory with Applications reveals intriguing new applications of number theory. This text details aspects of computer science related to Fundamental Number Theory with Applications also covers: Numerous exercises are included, testing the reader's knowledge of the concepts covered, introducing new and interesting topics, and providing a venue to learn background material. Written by a professor and author who is an accomplished scholar in this field, this book provides the material essential for an introduction to the fundamentals of number theory. |
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a₁ arithmetic assume base bit operations c(mod called Chapter class number computational congruences Conjecture continued fraction expansion contradiction Conversely Corollary defined Definition denoted Diophantine equations discriminant dividing division algorithm element elliptic curve equivalent Euler's Example Exercise exists Fermat's Little Theorem Fibonacci finite footnote function fundamental fundamental discriminant Gauss gcd(a gcd(m given Hence incongruent solutions induction hypothesis infinitely instance integer squares integral polynomial irreducible Legendre symbol Lemma mathematics method multiplicative inverse namely natural numbers notation notion number theory O-ideal odd prime P₁ pmod primality test prime divisor primitive representation primitive root modulo proof of Theorem Proposition Prove pseudoprime quadratic irrational quadratic orders quadratic residue quadratic residue modulo radicand reader relatively prime residue system modulo result Section simple continued fraction solutions modulo subtraction Suppose unique zero