Introduction to number theory /
Number theory
Richard Michael Hill, University College London, UK.
- xiv, 247 pages ; 24 cm.
- Essential textbooks in mathematics .
Textbook, with answers to some exercises.
Includes bibliographical references.
Machine generated contents note: 1.Euclid's Algorithm -- 1.1.Some Examples of Rings -- 1.2.Euclid's Algorithm -- 1.3.Invertible Elements Modulo n -- 1.4.Solving Linear Congruences -- 1.5.The Chinese Remainder Theorem -- 1.6.Prime Numbers -- Hints for Some Exercises -- 2.Polynomial Rings -- 2.1.Long Division of Polynomials -- 2.2.Highest Common Factors -- 2.3.Uniqueness of Factorization -- 2.4.Irreducible Polynomials -- 2.5.Unique Factorization Domains -- Hints for Some Exercises -- 3.Congruences Modulo Prime Numbers -- 3.1.Fermat's Little Theorem -- 3.2.The Euler Totient Function -- 3.3.Cyclotomic Polynomials and Primitive Roots -- 3.4.Public Key Cryptography -- 3.5.Quadratic Reciprocity -- 3.6.Congruences in an Arbitrary Ring -- 3.7.Proof of the Second Nebensatz -- 3.8.Gauss Sums and the Proof of Quadratic Reciprocity -- Hints for Some Exercises -- 4.p-Adic Methods in Number Theory -- 4.1.Hensel's Lemma -- 4.2.Quadratic Congruences -- 4.3.p-Adic Convergence of Series Note continued: 4.4.p-Adic Logarithms and Exponential Maps -- 4.5.Teichmuller Lifts -- 4.6.The Ring of p-Adic Integers -- Hints for Some Exercises -- 5.Diophantine Equations and Quadratic Rings -- 5.1.Diophantine Equations and Unique Factorization -- 5.2.Quadratic Rings -- 5.3.Norm-Euclidean Quadratic Rings -- 5.4.Decomposing Primes in Quadratic Rings -- 5.5.Continued Fractions -- 5.6.Pell's Equation -- 5.7.Real Quadratic Rings and Diophantine Equations -- Hints for Some Exercises -- Solution to Exercises.
College of Education Bachelor of Secondary Education major in Mathematics