mathematics, a generalized arithmetic progression (or multiple arithmetic progression) is a generalization of an arithmetic progression equipped with multiple...

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains...

small, then A {\displaystyle A} can be contained in a small generalized arithmetic progression. If A {\displaystyle A} is a finite subset of Z {\displaystyle...

arithmetic progression, the sum of the reciprocals of the prime numbers in the progression diverges and that different such arithmetic progressions with...

many 3 term arithmetic progressions. This was proven by Klaus Roth in 1952, and generalized to arbitrarily long arithmetic progressions by Szemerédi...

yields a geometric progression, while taking the logarithm of each term in a geometric progression yields an arithmetic progression. In mathematics, a...

The notion of an arithmetic progression topology can be generalized to arbitrary Dedekind domains. Two-sided arithmetic progressions in Z {\displaystyle...

theorem states that if a and d are coprime natural numbers, then the arithmetic progression a, a + d, a + 2d, a + 3d, ... contains infinitely many prime numbers...

Roth's theorem on arithmetic progressions is a result in additive combinatorics concerning the existence of arithmetic progressions in subsets of the...

density contains a k term arithmetic progression for every k. This conjecture, which became Szemerédi's theorem, generalizes the statement of van der Waerden's...

modulus of the progression. For example, 3, 12, 21, 30, 39, ..., is an infinite arithmetic progression with modulus 9. In an arithmetic progression, all the...

In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured...

Arithmetic progression – a sequence of numbers such that the difference between the consecutive terms is constant Generalized arithmetic progression –...

(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...

contains arbitrarily long arithmetic progressions. In other words, for every natural number k, there exist arithmetic progressions of primes with k terms...

1934, Chowla showed that the generalized Riemann hypothesis implies that the first prime in the arithmetic progression a mod m is at most Km2log(m)2...

conjecture is a conjecture about the distribution of prime numbers in arithmetic progressions. It has many applications in sieve theory. It is named for Peter...

on arithmetic progressions. It asserts that there exist positive c and L such that, if we denote p(a,d) the least prime in the arithmetic progression a...

Green and Terence Tao – the Green–Tao theorem, that there are arithmetic progressions of primes of arbitrary length – there is no general result known...

largest known Generalized Fermat prime to date, 19637361048576 + 1. This prime is 6,598,776 digits long and is only the second Generalized Fermat prime...

lengths of a generalized Brahmagupta triangle which form an arithmetic progression with common difference k {\displaystyle k} . There are generalized Brahmagupta...

character Dirichlet L-series Siegel zero Dirichlet's theorem on arithmetic progressions Linnik's theorem Elliott–Halberstam conjecture Functional equation...

introduced the Dirichlet characters and L-functions. In 1841 he generalized his arithmetic progressions theorem from integers to the ring of Gaussian integers...

mathematicians. This theorem states that there are arbitrarily long arithmetic progressions of prime numbers. The New York Times described it this way: In...

find all of the smaller primes. It may be used to find primes in arithmetic progressions. Sift the Two's and Sift the Three's: The Sieve of Eratosthenes...

First Hardy–Littlewood conjecture Prime constellation Primes in arithmetic progression Dickson, L. E. (1904), "A new extension of Dirichlet's theorem on...

Erdős–Selberg argument". Let πd,a(x) denote the number of primes in the arithmetic progression a, a + d, a + 2d, a + 3d, ... that are less than x. Dirichlet and...

primes today are generalized Fermat primes. Generalized Fermat numbers can be prime only for even a, because if a is odd then every generalized Fermat number...

principles of arithmetic presented by a new method (Latin: Arithmetices principia, nova methodo exposita). This approach is now called Peano arithmetic. It is...

Binary Progression", in 1679, Leibniz introduced conversion between decimal and binary, along with algorithms for performing basic arithmetic operations...