számelméletnek

Számelméletnek is the Hungarian word for number theory. It is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. It is concerned with the properties of integers, such as divisibility, prime numbers, Diophantine equations, and congruences.

Historically, number theory has been divided into several subfields. The most accessible parts of the subject concern the integers themselves and are called elementary number theory. This area includes the study of divisibility, prime numbers, the Euclidean algorithm, and modular arithmetic. Analytic number theory uses the tools of mathematical analysis to study problems about integers. Prime number theory is a major part of analytic number theory, concerned with the distribution of prime numbers. Algebraic number theory studies the properties of integers in algebraic number fields. Geometric number theory involves the study of integer points in geometric structures.

The study of number theory has a long and rich history, with contributions from mathematicians across the globe. Ancient Greek mathematicians like Euclid and Diophantus made early contributions. Later, mathematicians such as Fermat, Euler, Gauss, and Riemann significantly advanced the field. Modern number theory continues to be an active area of research, with connections to cryptography, computer science, and other branches of mathematics.