Number Theory - Structures, Examples and Problems

Number theory, branch of mathematics concerned with properties of the positive integers. Sometimes called higher arithmetic, it is among the oldest and most natural of mathematical pursuits. Number theory has always fascinated amateurs as well as professional mathematicians. In contrast to other branches of mathematics, many of the problems and theorems of number theory can be understood by laypersons, although solutions to the problems and proofs of the theorems often require a sophisticated mathematical background. Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and prime factorisation are especially important in number theory, as are a number of functions such as the divisor function, Riemann zeta function, and totient function. Number theory is an ongoing rich area of mathematical exploration with connections and applications to other fields from representation theory, to physics, cryptography, and more. While the forefront of number theory is replete with sophisticated and famous open problems, at its foundation are basic, elementary ideas that can stimulate and challenge beginning students. This book Number Theory - Structures, Examples and Problems focuses on a problem-solving approach to the subject.