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

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

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.

ter's conjecture is a conjecture in combinatorial number theory, named after the British mathematician David Singmaster who propos

of the most famous open problems in the topic of number theory.

Lehmer's Mahler measure problem, is a problem in number theory raised by Derrick Henry Lehmer.

In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, diviso

In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing

In number theory, a prime number p is a Sophie Germain prime if 2p + 1 is also prime.

In number theory, Dirichlet's theorem on Diophantine approximation, also called Dirichlet's approximation theorem, states that for

In algebra and number theory, Euclid's lemma is a lemma that captures a fundamental property of prime numbers: For example, if p =

Fermat's Last Theorem is a theorem in number theory, originally stated by Pierre de Fermat in 1637 and proven by Andrew Wiles in 1

In number theory, Chen's theorem states that every sufficiently large even number can be written as the sum of either two primes o

In number theory, Maier's theorem is a theorem due to Helmut Maier about the numbers of primes in short intervals for which Cramér

In number theory, Mazur's control theorem, introduced by Mazur (1972), describes the behavior in Zp extensions of the Selmer group

In mathematics, and specifically in number theory, a divisor function is an arithmetic function related to the divisors of an inte

In mathematics, specifically transcendental number theory, the six exponentials theorem is a result that, given the right conditio

In number theory, the sum of the first n cubes is the square of the nth triangular number.

In arithmetic and number theory, the least common multiple (LCM), lowest common multiple, or smallest common multiple (SCM) of two

In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose domain is the set of p

In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides.

In mathematics, and more specifically number theory, the superfactorial of a positive integer n is the product of the first n fact

In number theory, a weird number is a natural number that is abundant but not semiperfect.

In number theory, Lemoine's conjecture, also sometimes known as Levy's conjecture, states that all odd integers greater than 5 can

In number theory, Firoozbakht's conjecture (or the Firoozbakht conjecture) is a conjecture about the distribution of prime numbers

In mathematics, specifically in number theory, Grimm's conjecture states that, for every set of consecutive composite numbers, the

In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian v

In number theory, Agrawal's conjecture, due to Manindra Agrawal in 2002, forms the basis for the cyclotomic AKS test.

ematics, specifically the field of transcendental number theory, the four exponentials conjecture is a conjecture which, given the

njecture in additive combinatorics and elementary number theory about an upper bound for the number of squares in finite arithmeti

In mathematics, specifically number theory, Serre's conjecture II is the statement that if G is a simply connected, semisimple alg

In number theory, Polignac's conjecture was made by Alphonse de Polignac in 1849 and states: For any positive even number n, there

Gilbreath's conjecture is a conjecture in number theory regarding the sequences generated by applying the forward difference opera

In number theory, the Stark conjectures, introduced by Stark (1971, 1975, 1976, 1980) and later expanded by Tate (1984), give conj

In number theory, Szpiro's conjecture relates the conductor of an elliptic curve to its discriminant.

In number theory, given a prime number p, the p-adic numbers form an extension of the rational numbers that is distinct from the r

In number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n .

In transcendental number theory, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of linear c

In number theory, an integer q is a quadratic residue modulo n if it is congruent to a perfect square modulo n; that is, if there

In number theory, Zsigmondy's theorem, named after Karl Zsigmondy, states that if a > b > 0 are coprime integers, then for any int

In number theory, the Heegner theorem or Stark-Heegner theorem establishes the complete list of the quadratic imaginary number fie

In number theory, Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime.

In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most n n-gonal nu

In number theory, Tunnell's theorem gives a partial resolution to the congruent number problem, and under the Birch and Swinnerton

In number theory, Hilbert's irreducibility theorem, conceived by David Hilbert in 1892, states that every finite set of irreducibl

In mathematics, particularly in number theory, Hillel Furstenberg's proof of the infinitude of primes is a topological proof that

In number theory, Carmichael's theorem, named after the American mathematician R.

In number theory, Glaisher's theorem is an identity useful to the study of integer partitions.

In number theory, the Hasse norm theorem states that if L/K is a cyclic extension of number fields, then if a nonzero element of K

In number theory, Lochs's theorem concerns the rate of convergence of the continued fraction expansion of a typical real number.

In additive number theory, the Schnirelmann density of a sequence of numbers is a way to measure how "dense" the sequence is.

In number theory, Proth's theorem is a theorem which forms the basis of a primality test for Proth numbers known as Proth's test.

In number theory, Tijdeman's theorem states that there are at most a finite number of consecutive powers.

uality is a mathematical theorem in probabilistic number theory.

In number theory, Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the f

number theory

transcendental number theory

Lucas sequences and Lucas numbers

In number theory

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number theory

the geometry of numbers

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number theory

number theory

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number theory