{"product_id":"elementary-number-theory-9781292039541","title":"Elementary Number Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cb\u003eP. What is Number Theory?\u003c\/b\u003e \u003cbr\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e1. The Integers.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eNumbers and Sequences. \u003cp\u003e \u003c\/p\u003eSums and Products. \u003cp\u003e \u003c\/p\u003eMathematical Induction. \u003cp\u003e \u003c\/p\u003eThe Fibonacci Numbers. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e2. Integer Representations and Operations.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eRepresentations of Integers. \u003cp\u003e \u003c\/p\u003eComputer Operations with Integers. \u003cp\u003e \u003c\/p\u003eComplexity of Integer Operations. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e3. Primes and Greatest Common Divisors.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003ePrime Numbers. \u003cp\u003e \u003c\/p\u003eThe Distribution of Primes. \u003cp\u003e \u003c\/p\u003eGreatest Common Divisors. \u003cp\u003e \u003c\/p\u003eThe Euclidean Algorithm. \u003cp\u003e \u003c\/p\u003eThe Fundemental Theorem of Arithmetic. \u003cp\u003e \u003c\/p\u003eFactorization Methods and Fermat Numbers. \u003cp\u003e \u003c\/p\u003eLinear Diophantine Equations. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e4. Congruences.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eIntroduction to Congruences. \u003cp\u003e \u003c\/p\u003eLinear Congrences. \u003cp\u003e \u003c\/p\u003eThe Chinese Remainder Theorem. \u003cp\u003e \u003c\/p\u003eSolving Polynomial Congruences. \u003cp\u003e \u003c\/p\u003eSystems of Linear Congruences. \u003cp\u003e \u003c\/p\u003eFactoring Using the Pollard Rho Method. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e5. Applications of Congruences.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eDivisibility Tests. \u003cp\u003e \u003c\/p\u003eThe perpetual Calendar. \u003cp\u003e \u003c\/p\u003eRound Robin Tournaments. \u003cp\u003e \u003c\/p\u003eHashing Functions. \u003cp\u003e \u003c\/p\u003eCheck Digits. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e6. Some Special Congruences.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eWilson's Theorem and Fermat's Little Theorem. \u003cp\u003e \u003c\/p\u003ePseudoprimes. \u003cp\u003e \u003c\/p\u003eEuler's Theorem. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e7. Multiplicative Functions.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eThe Euler Phi-Function. \u003cp\u003e \u003c\/p\u003eThe Sum and Number of Divisors. \u003cp\u003e \u003c\/p\u003ePerfect Numbers and Mersenne Primes. \u003cp\u003e \u003c\/p\u003eMobius Inversion. \u003cbr\u003ePartitions. \u003cbr\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e8. Cryptology.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eCharacter Ciphers. \u003cp\u003e \u003c\/p\u003eBlock and Stream Ciphers. \u003cp\u003e \u003c\/p\u003eExponentiation Ciphers. \u003cp\u003e \u003c\/p\u003eKnapsack Ciphers. \u003cp\u003e \u003c\/p\u003eCryptographic Protocols and Applications. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e9. Primitive Roots.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eThe Order of an Integer and Primitive Roots. \u003cp\u003e \u003c\/p\u003ePrimitive Roots for Primes. \u003cp\u003e \u003c\/p\u003eThe Existence of Primitive Roots. \u003cp\u003e \u003c\/p\u003eIndex Arithmetic. \u003cp\u003e \u003c\/p\u003ePrimality Tests Using Orders of Integers and Primitive Roots. \u003cp\u003e \u003c\/p\u003eUniversal Exponents. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e10. Applications of Primitive Roots and the Order of an Integer.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003ePseudorandom Numbers. \u003cp\u003e \u003c\/p\u003eThe EIGamal Cryptosystem. \u003cp\u003e \u003c\/p\u003eAn Application to the Splicing of Telephone Cables. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e11. Quadratic Residues.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eQuadratic Residues and nonresidues. \u003cp\u003e \u003c\/p\u003eThe Law of Quadratic Reciprocity. \u003cp\u003e \u003c\/p\u003eThe Jacobi Symbol. \u003cp\u003e \u003c\/p\u003eEuler Pseudoprimes. \u003cp\u003e \u003c\/p\u003eZero-Knowledge Proofs. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e12. Decimal Fractions and Continued.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eDecimal Fractions. \u003cp\u003e \u003c\/p\u003eFinite Continued Fractions. \u003cp\u003e \u003c\/p\u003eInfinite Continued Fractions. \u003cp\u003e \u003c\/p\u003ePeriodic Continued Fractions. \u003cp\u003e \u003c\/p\u003eFactoring Using Continued Fractions. \u003cbr\u003e \u003cbr\u003e \u003cb\u003e13. Some Nonlinear Diophantine Equations.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003ePythagorean Triples. \u003cp\u003e \u003c\/p\u003eFermat's Last Theorem. \u003cp\u003e \u003c\/p\u003eSums of Squares. \u003cp\u003e \u003c\/p\u003ePell's Equation. \u003cbr\u003eCongruent Numbers. \u003cbr\u003e \u003cbr\u003e \u003cbr\u003e \u003cb\u003e14. The Gaussian Integers.\u003c\/b\u003e \u003cbr\u003e \u003cp\u003e \u003c\/p\u003eGaussian Primes. \u003cp\u003e \u003c\/p\u003eUnique Factorization of Gaussian Integers. \u003cp\u003e \u003c\/p\u003eGaussian Integers and Sums of Squares.","brand":"Pearson Education","offers":[{"title":"Default Title","offer_id":51039303205207,"sku":"9781292039541","price":71.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781292039541.jpg?v=1750943244","url":"https:\/\/bookcurl.com\/products\/elementary-number-theory-9781292039541","provider":"Book Curl","version":"1.0","type":"link"}