Számelméleti

Számelméleti is the Hungarian term for Number Theory. It is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. Classic number theory is concerned with the properties of integers, such as divisibility, prime numbers, Diophantine equations, and congruences. It explores the relationships between numbers and their patterns.

The field of number theory can be broadly divided into several areas. Elementary number theory involves proving properties of integers without the use of techniques from other advanced mathematical fields. Analytic number theory uses methods from mathematical analysis to study integers, for example, the distribution of prime numbers. Algebraic number theory generalizes the concept of integers to algebraic integers and studies their properties. Probabilistic number theory deals with the distribution of numbers with specific properties, often using probabilistic methods.

Historically, number theory has been a source of many fundamental mathematical discoveries and has found applications in diverse fields such as cryptography, computer science, and physics. The study of prime numbers, for instance, is a central theme that has captivated mathematicians for centuries due to its inherent complexity and profound implications.