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《初等数论及其应用(英文版)(第6版)》是数论课程的经典教材，自出版以来，深受读者好评，被美国加州大学伯克利分校、伊利诺伊大学、得克萨斯大学等数百所名校采用。

《初等数论及其应用(英文版)(第6版)》以经典理论与现代应用相结合的方式介绍了初等数论的基本概念和方法，内容包括整除、同余、二次剩余、原根以及整数的阶的讨论和计算。

Kenneth H．Rosen密歇根大学数学学士，麻省理工学院数学博士。曾就职于科罗拉多大学，俄亥俄州立大学，缅因大学，后加盟贝尔实验室，现为AT&T实验室特别成员。Rosen博士在数论领域与数学建模领域著有大量的论文及专著，除本书外，还著有经典作品《离散数学及其应用》 （本书中文版、影印版已由机械工业出版社引进出版）。此外，他还担任CRC出版社离散数学丛书的主编。

1 the integers
1.1 numbers and sequences
1.2 sums and products
1.3 mathematical induction
1.4 the fibonacci numbers
1.5 divisibility
2 integer representations and operations
2.1 representations of integers
2.2 computer operations with integers
2.3 complexity of integer operations
3 primes and greatest common divisors
3.1 prime numbers
3.2 the distribution of primes
3.3 greatest common divisors and their properties
3.4 the euclidean algorithm
3.5 the fundamental theorem of arithmetic
3.6 factorization methods and the fermat numbers
3.7 linear diophantine equations
4 congruences
4.1 introduction to congruences
4.2 linear congruences
4.3 the chinese remainder theorem
4.4 solving polynomial congruences
4.5 systems of linear congruences
4.6 factoring using the pollard rho method
5 applications of congruences
5.1 divisibility tests
5.2 the perpetual calendar
5.3 round-robin tournaments
5.4 hashing functions
5.5 check digits
6 some special congruences
6.1 wilsons theorem and fermats little theorem
6.2 pseudoprimes
6.3 eulers theorem
7 multiplicative functions
7.1 the euler phi-function
7.2 the sum and number of divisors
7.3 perfect numbers and mersenne primes
7.4 misbius inversion
7.5 partitions
8 cryptology
8.1 character ciphers
8.2 block and stream ciphers
8.3 exponentiation ciphers
8.4 public key cryptography
8.5 knapsack ciphers
8.6 cryptographic protocols and applications
9 primitive roots
9.1 the order of an integer and primitive roots
9.2 primitive roots for primes
9.3 the existence of primitive roots
9.4 discrete logarithms and index arithmetic
9.5 primality tests using orders of integers and primitive roots
9.6 universal exponents
10 applications of primitive roots and the order of an integer
10.1 pseudorandom numbers
10.2 the eigamal cryptosystem
10.3 an application to the splicing of telephone cables
11 quadratic residues
11.1 quadratic residues and nonresidues
11.2 the law of quadratic reciprocity
11.3 the jacobi symbol
11.4 euler pseudoprimes
11.5 zero-knowledge proofs
12 decimal fractions and continued fractions
12.1 decimal fractions
12.2 finite continued fractions
12.3 infinite continued fractions
12.4 periodic continued fractions
12.5 factoring using continued fractions
13 some nonlinear diophantine equations
13.1 pythagorean triples
13.2 fermats last theorem
13.3 sums of squares
13.4 pells equation
13.5 congruent numbers
14 the gaussian integers
14.1 gaussian integers and gaussian primes
14.2 greatest common divisors and unique factorization
14.3 gaussian integers and sums of squares
appendix a axioms for the set of integers
appendix b binomial coefficients
appendix c using maple and mathematica for number theory
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