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...

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...

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

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

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

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

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...

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

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

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

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

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...

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

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

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

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

number of numbers in the collection. Arithmetic progression In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers...

_{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 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...

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

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...

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

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...

calculating the sum of the first n {\displaystyle n} terms of an arithmetic progression. In chronological order, early discoveries include: 1 + 2 + ⋯ +...

be the only minimal difference greater than 1 of any increasing arithmetic progression of n primes (in this case, n = 7) that is not a primorial (a product...

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