Number Theory

Historically areas often considered attached to pure mathematics are number theory, where these infinities are typically countable and algebraic geometry where functions are typically tamed functions.

Number theory is the branch of mathematics that studies integers and their properties and relations.

It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs.

if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers

The conjecture is one of Landau's problems (1912) on prime numbers

The Beal conjecture is the following conjecture in number theory

Born (1931-09-25) 25 September 1931 (age 94) Burton-upon-Trent, England ... Awards Senior Whitehead Prize (1993) De Morgan Medal (2007) Sylvester Medal (2020)

David William Masser is professor emeritus in the Department of Mathematics and Computer Science at the University of Basel. He is known for his work in transcendental number theory, Diophantine approximation, and Diophantine geometry. With Joseph Oesterle in 1985, Masser formulated the abc conjecture, which has been called the most important unsolved problem in Diophantine analysis.

Shinichi Mochizuki is a Japanese mathematician working in number theory and arithmetic geometry. He is one of the main contributors to anabelian geometry.

Tom Cusick's research is in cryptography, especially Boolean function applications; number theory, particularly Diophantine approximation and algebraic number theory; and combinatorics.

every integer greater than 1 can be represented uniquely as a product of prime numbers

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers.

The question of whether there exist infinitely many twin primes has been one of the great open questions in number theory for many years.

one of the oldest and best-known unsolved problems in number theory and all of mathematics

Unsolved problems in number theory

It is of great interest in number theory because it implies results about the distribution of prime numbers.

the Birch and Swinnerton-Dyer conjecture describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory

The Erdos-Straus conjecture is an unproven statement in number theory.

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a, b, c, n with n > 2 such that a^n + b^n = c^n.