Additive number theory information

Additive number theory is the subfield of number theory concerning the study of subsets of integers and their behavior under addition. More abstractly...

progressions. Additive number theory is concerned with the additive structure of the integers, such as Goldbach's conjecture that every even number greater...

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

example, groups, rings and fields. Additive number theory Approximate group Corners theorem Ergodic Ramsey theory Problems involving arithmetic progressions...

combinatorics. This is a presently coalescing field; it subsumes additive number theory (which concerns itself with certain very specific sets A {\displaystyle...

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

In number theory, the sum of two squares theorem relates the prime decomposition of any integer n > 1 to whether it can be written as a sum of two squares...

is not a number, but the source of number. He also believed the number two is the embodiment of the origin of otherness. His number theory was recovered...

discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential...

n} summands. Many of the questions and results of additive combinatorics and additive number theory can be phrased in terms of sumsets. For example, Lagrange's...

is a number representing an empty quantity. Adding 0 to any number leaves that number unchanged. In mathematical terminology, 0 is the additive identity...

as the sum of six primes. The branch of number theory studying such questions is called additive number theory. Another type of problem concerns prime...

A characterization of Pythagorean triples, JP Journal of Algebra, Number Theory and Applications 39 (2) (2017), 221-230. MacHale, Des, and van den Bosch...

number theory" (PDF), Notices of the American Mathematical Society, 55 (3): 344–350, MR 2382821 Dickson, Leonard Eugene (1920), History of the Theory...

In additive number theory, an additive basis is a set S {\displaystyle S} of natural numbers with the property that, for some finite number k {\displaystyle...

In mathematics, the additive polynomials are an important topic in classical algebraic number theory. Let k be a field of prime characteristic p. A polynomial...

In additive number theory and combinatorics, a restricted sumset has the form S = { a 1 + ⋯ + a n :   a 1 ∈ A 1 , … , a n ∈ A n   a n d   P ( a 1 , … ...

such a quadratic form taking all other 8 positive integers except for this number as values. For example, the quadratic form w 2 + x 2 + y 2 + z 2 {\displaystyle...

the Erdős–Kac theorem on additive functions. Number theory Analytic number theory Areas of mathematics List of number theory topics List of probability...

his name, such as Dyson's transform, a fundamental technique in additive number theory, which he developed as part of his proof of Mann's theorem; the...

In number theory, an additive function is an arithmetic function f(n) of the positive integer variable n such that whenever a and b are coprime, the function...