• Thumbnail for Arithmetic progression
    An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains...
    13 KB (2,296 words) - 18:12, 19 November 2024
  • arithmetic progression, the sum of the reciprocals of the prime numbers in the progression diverges and that different such arithmetic progressions with...
    24 KB (3,524 words) - 05:25, 14 December 2024
  • Thumbnail for Geometric progression
    yields a geometric progression, while taking the logarithm of each term in a geometric progression yields an arithmetic progression. In mathematics, a...
    9 KB (1,544 words) - 18:39, 10 October 2024
  • primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression. An example...
    17 KB (1,597 words) - 06:23, 5 November 2024
  • 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...
    66 KB (9,138 words) - 04:56, 16 December 2024
  • Thumbnail for Prime number
    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...
    117 KB (14,199 words) - 07:41, 21 December 2024
  • Thumbnail for Magic square
    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...
    281 KB (22,268 words) - 23:16, 21 October 2024
  • positive integers by taking as a base a suitable collection of arithmetic progressions, sequences of the form { b , b + a , b + 2 a , . . . } {\displaystyle...
    13 KB (1,732 words) - 07:56, 15 October 2024
  • mathematics, a generalized arithmetic progression (or multiple arithmetic progression) is a generalization of an arithmetic progression equipped with multiple...
    3 KB (548 words) - 04:04, 20 November 2024
  • In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured...
    22 KB (2,490 words) - 17:18, 8 December 2024
  • Erdős' conjecture on arithmetic progressions, often referred to as the Erdős–Turán conjecture, is a conjecture in arithmetic combinatorics (not to be...
    7 KB (895 words) - 12:45, 10 November 2024
  • Problems involving arithmetic progressions are of interest in number theory, combinatorics, and computer science, both from theoretical and applied points...
    5 KB (622 words) - 17:06, 13 August 2023
  • arbitrarily long arithmetic progressions. In other words, for every natural number k {\displaystyle k} , there exist arithmetic progressions of primes with...
    13 KB (1,538 words) - 17:54, 30 November 2024
  • The arithmetic progression game is a positional game where two players alternately pick numbers, trying to occupy a complete arithmetic progression of...
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  • Thumbnail for Harmonic progression (mathematics)
    mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression, which is also known...
    5 KB (699 words) - 04:40, 3 December 2024
  • Roth's theorem on arithmetic progressions is a result in additive combinatorics concerning the existence of arithmetic progressions in subsets of the...
    28 KB (4,548 words) - 18:11, 10 October 2024
  • Look up progression in Wiktionary, the free dictionary. Progression may refer to: In mathematics: Arithmetic progression, a sequence of numbers such that...
    2 KB (299 words) - 15:42, 25 August 2024
  • Thumbnail for Number theory
    (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...
    86 KB (10,828 words) - 12:00, 12 December 2024
  • _{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...
    23 KB (4,572 words) - 08:48, 9 December 2024
  • 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...
    34 KB (8,032 words) - 08:16, 2 December 2024
  • approximation, Roth made major contributions to the theory of progression-free sets in arithmetic combinatorics and to the theory of irregularities of distribution...
    30 KB (3,359 words) - 16:11, 11 November 2024
  • prime numbers contains arbitrarily long arithmetic progressions. In other words, there exist arithmetic progressions of primes, with k terms, where k can...
    9 KB (956 words) - 03:03, 2 November 2024
  • 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...
    30 KB (3,762 words) - 10:56, 19 January 2024
  • Thumbnail for Special right triangle
    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...
    20 KB (1,677 words) - 09:50, 18 July 2024
  • Thumbnail for Cube (algebra)
    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...
    24 KB (3,006 words) - 05:25, 7 September 2024
  • 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...
    11 KB (1,175 words) - 05:35, 16 December 2024
  • 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...
    8 KB (845 words) - 17:56, 12 August 2023
  • Thumbnail for Congruum
    congrua) is the difference between successive square numbers in an arithmetic progression of three squares. That is, if x 2 {\displaystyle x^{2}} , y 2 {\displaystyle...
    8 KB (1,018 words) - 22:49, 10 December 2022
  • Thumbnail for Analytic number theory
    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...
    27 KB (3,832 words) - 07:28, 14 December 2024
  • 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...
    18 KB (2,928 words) - 15:16, 21 November 2024