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...

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

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

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

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...

yields a geometric progression, while taking the logarithm of each term in a geometric progression yields an arithmetic progression. The relation that...

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...

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

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

19th century result was Dirichlet's theorem on arithmetic progressions, that certain arithmetic progressions contain infinitely many primes. Many mathematicians...

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

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

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...

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

arbitrarily long arithmetic progressions. In other words, for every natural number k {\displaystyle k} , there exist arithmetic progressions of primes with...

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

numbers in an arithmetic progression of three squares. The congruum problem is the problem of finding squares in arithmetic progression and their associated...

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

of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties...

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...

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

multiplication of the elements of a geometric progression with the corresponding elements of an arithmetic progression. The nth element of an arithmetico-geometric...

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...

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...

avoid arithmetic progressions. If S {\displaystyle S} is a finite set of non-negative integers on which no three elements form an arithmetic progression (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...

valid progression of points or weightings may be chosen at will (Eurovision Song Contest) or it may form a mathematical sequence such as an arithmetic progression...

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...

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...