Advanced Number Theory with Applications

By covering a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory, this text provides the most up-to-date and comprehensive material for a second course in this field. With numerous examples and exercises, it begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes. The author then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. He also presents Fermat's Last Theorem, the ABC conjecture, and sieve methods.