Books like A Classical Introduction to Modern Number Theory by Kenneth F. Ireland

Karl Sabbagh explores the Riemann hypothesis, the foundational conjecture in number theory that predicts the distribution of prime numbers and the structure of integers. This enduring mathematical mystery remains unproven.

The Higher Arithmetic presents number theory concepts and theorems through clear, accessible exposition, with new material on Fermat’s Last Theorem, computational methods, and primality testing.

This textbook covers the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. This book excludes topics relying heavily on complex analysis and advanced algebraic number theory. The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on Fermat's last theorem is also briefly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables.