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Pisot–Vijayaraghavan number. Salem number. Transcendental number. e (mathematical constant) pi, list of topics related to pi. Squaring the circle. Proof that e is irrational. Lindemann–Weierstrass theorem. Hilbert's seventh problem.
Mathematics. 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 .
Noncommutative algebra. v. t. e. Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation with rational coefficients), in both qualitative and quantitative ways.
In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.)
The Erdős–Straus conjecture is an unproven statement in number theory. The conjecture is that, for every integer that is 2 or more, there exist positive integers , , and for which In other words, the number can be written as a sum of three positive unit fractions.
Apéry's theorem. In mathematics, Apéry's theorem is a result in number theory that states the Apéry's constant ζ (3) is irrational. That is, the number. cannot be written as a fraction where p and q are integers. The theorem is named after Roger Apéry. The special values of the Riemann zeta function at even integers ( ) can be shown in ...
In number theory, Hurwitz's theorem, named after Adolf Hurwitz, gives a bound on a Diophantine approximation. The theorem states that for every irrational number ξ there are infinitely many relatively prime integers m, n such that. The condition that ξ is irrational cannot be omitted. Moreover the constant is the best possible; if we replace ...
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