A Course in Number Theory

This textbook deals with the central topics in number theory as taught in universities throughout the world. Number theory is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent subtheories and a long list of unsolved problems. Excluding topics which rely heavily on more advanced complex analysis and algebraic number theory this book considers eight central areas: divisibility and multiplicative functions; congruences and quadratic residues; an introduction to algebraic numbers and sums of squares; continued fractions, diophantine approximation and transducence; quadratic forms; partitions; the prime numbers; diophantine equations and elliptic curves. Some more advanced results are also given including the Gelfond-Schneider theorem, the prime number theorem and the Mordell-Weil theorem. Each chapter ends with a collection of problems; hints or sketch solutions are given at the back of the book together with various tables.