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

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

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

primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression. An example...

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...

positive integers by taking as a base a suitable collection of arithmetic progressions, sequences of the form { b , b + a , b + 2 a , . . . } {\displaystyle...

of s arithmetic progressions with the same common difference among r terms, such that r × s = n2, and whose initial terms are also in arithmetic progression...

Erdős' conjecture on arithmetic progressions, often referred to as the Erdős–Turán conjecture, is a conjecture in arithmetic combinatorics (not to be...

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...

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

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

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

mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression. Equivalently, a sequence...

of the calculation of the arithmetic series, the sum of the first n {\displaystyle n} values of an arithmetic progression. This problem is quite simple...

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

(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...

Problems involving arithmetic progressions are of interest in number theory, combinatorics, and computer science, both from theoretical and applied points...

Look up progression in Wiktionary, the free dictionary. Progression may refer to: In mathematics: Arithmetic progression, a sequence of numbers such that...

_{i=0}^{n}i=\sum _{i=1}^{n}i={\frac {n(n+1)}{2}}\qquad } (Sum of the simplest arithmetic progression, consisting of the first n natural numbers.): 52  ∑ i = 1 n ( 2...

The arithmetic progression game is a positional game where two players alternately pick numbers, trying to occupy a complete arithmetic progression of...

an arithmetic progression. The proof of this fact is simple and follows on from the fact that if α, α + δ, α + 2δ are the angles in the progression then...

prime numbers contains arbitrarily long arithmetic progressions. In other words, there exist arithmetic progressions of primes, with k terms, where k can...

the same color form an arithmetic progression. But you can't add a ninth integer to the end without creating such a progression. If you add a red 9, then...

approximation, Roth made major contributions to the theory of progression-free sets in arithmetic combinatorics and to the theory of irregularities of distribution...

in particular in arithmetic combinatorics, a Salem-Spencer set is a set of numbers no three of which form an arithmetic progression. Salem–Spencer sets...

k-tuple of the form (0, n, 2n, 3n, …, (k − 1)n) is said to be a prime arithmetic progression. In order for such a k-tuple to meet the admissibility test, n must...

In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number...

L-functions to give the first proof of Dirichlet's theorem on arithmetic progressions. It is well known for its results on prime numbers (involving the...

the sum of the arithmetic progression used divided by the order of the magic square. It is possible not to start the arithmetic progression from the middle...

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...