Elementary number theory and its applications
This latest edition of Kenneth Rosen's widely used "Elementary Number Theory and Its Applications" enhances the flexibility and depth of previous editions while preserving their strengths. Rosen effortlessly blends classic theory with contemporary applications. New examples, additional applications and increased cryptology coverage are also included. The book has also been accuracy-checked to ensure the quality of the content. A diverse group of exercises are presented to help develop skills. Also included are computer projects. The book contains updated and increased coverage of Cryptography and new sections on Mobius Inversion and solving Polynomial Congruences. Historical content has also been enhanced to show the history for the modern material. For those interested in number theory.
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What is Number Theory?
Integer Representations and Operations
Primes and Greatest Common Divisors
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arithmetic base b expansion bit operations Carmichael number cipher ciphertext computation program Computational and Programming Computations and Explorations conjecture Corollary cryptosystem decimal expansion decrypting diophantine equation divides division algorithm encrypted Euclidean algorithm Euler pseudoprime exponent Fermat numbers Fermat's little theorem Fibonacci numbers following computations formula function greatest common divisor Hence incongruent solutions inverse law of quadratic least positive residue Lemma linear congruences Maple or Mathematica mathematical induction Mersenne primes method multiplicative notation number theory obtain odd prime pairs plaintext polynomial primality test prime divisor prime factorization prime number prime-power factorization primitive root modulo Programming Exercises Computations Programming Projects Write programs using Maple Projects Write programs proof prove pseudorandom numbers Pythagorean triple quadratic irrational quadratic nonresidue quadratic reciprocity quadratic residue rational numbers real number relatively prime residues modulo Section sequence Show simple continued fraction strong pseudoprime Suppose