Number Theory

Number Theory occupies a central position in mathematics, distinguished by its focus on the structure, properties, and relationships of integers. Historically rooted in ancient civilizations and advanced through the works of mathematicians such as Euclid, Fermat, Euler, and Gauss, the subject has continuously evolved while retaining its classical charm. Its problems are often simple to formulate yet demand deep insight and creativity, reflecting the unique intellectual appeal of the discipline. This book aims to present Number Theory in a clear, rigorous, and progressive manner, guiding readers from foundational concepts to more advanced topics. Core areas such as divisibility, prime numbers, greatest common divisors, congruences, arithmetic functions, quadratic residues, and Diophantine equations are treated systematically. Wherever possible, proofs are developed step by step to enhance conceptual clarity, while examples and exercises are carefully selected to strengthen problem-solving skills.