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Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." [1]
Sejarah teori bilangan aljabar. Diophantus. Awal mulanya teori bilangan aljabar dapat ditelusuri kembali dari persamaan Diophantine. [1] . Nama dari persamaan tersebut diambil dari seorang ahli matematika Aleksandria pada abad ke-3, Diophantus, yang mempelajarinya dan mengembangkan metode untuk solusi dari beberapa jenis persamaan Diophantine.
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Dalam matematika, teori bilangan analitik ( bahasa Inggris: analytic number theory) adalah sebuah cabang dari teori bilangan yang menggunakan metode analisis matematika untuk menyelesaikan masalah terkait bilangan bulat. [1] .
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers , finite fields , and function fields .
In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet 's 1837 introduction of Dirichlet L -functions to give the first proof of Dirichlet's theorem on arithmetic progressions .
Properties of the natural numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics .
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