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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]
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 .
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Apr 11, 2024 · A glance at Paulo Ribenboim's Fermat's Last Theorem for amateurs, Franz Lemmermeyer's Reciprocity Laws and L.E. Dickson's History of the Theory of Numbers, reveals the existence of many past number theorists about whom little is known.
Number theory. Several of his early papers also deal with questions of number theory. Lagrange (1766–1769) was the first European to prove that Pell's equation x 2 − ny 2 = 1 has a nontrivial solution in the integers for any non-square natural number n.
Apr 18, 2024 · Harald August Bohr (born April 22, 1887, Copenhagen, Den.—died Jan. 22, 1951, Copenhagen) was a Danish mathematician who devised a theory that concerned generalizations of functions with periodic properties, the theory of almost periodic functions.
- The Editors of Encyclopaedia Britannica
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.
Jun 6, 2020 · Number theory. The science of integers (cf. also Integer ). Integers, together with the simplest geometrical figures, were the first and the most ancient mathematical concepts. Number theory arose from problems in arithmetic connected with the multiplication and division of integers.
