# arithmetic progression

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Related to Arithmetic progressions: geometric progressions

## arithmetic progression

n.
A sequence, such as the positive odd integers 1, 3, 5, 7, ... , in which each term after the first is formed by adding a constant to the preceding term.

## arithmetic progression

n
(Mathematics) a sequence of numbers or quantities, each term of which differs from the succeeding term by a constant amount, such as 3,6,9,12. Compare geometric progression
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## arithmet′ic progres′sion

n.
a sequence in which each term is obtained by the addition of a constant number to the preceding term, as 1, 4, 7, 10, and 6, 1, −4, −9. Also called ar′ithmet′ic se′ries.

## ar·ith·met·ic progression

(ăr′ĭth-mĕt′ĭk)
A sequence of numbers such as 1, 3, 5, 7, 9 ..., in which each term after the first is formed by adding a constant to the preceding number (in this case, 2). Compare geometric progression.

## arithmetic progression

- A sequence in which each term is obtained by the addition of a constant number to the preceding term, as 1, 4, 7, 10, 13.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 arithmetic progression - (mathematics) a progression in which a constant is added to each term in order to obtain the next term; "1-4-7-10-13- is the start of an arithmetic progression"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementpatterned advance, progression - a series with a definite pattern of advance
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References in periodicals archive ?
Looking in turn at elementary methods, complex analysis methods, and probabilistic methods, he considers such topics as prime numbers, arithmetic functions, sieve methods, the method of van der Corput, the Euler gamma function, summation formulae, the prime number theorem and the Riemann hypothesis, two arithmetic application, primes in arithmetic progressions, densities, distributions of additive functions and mean values of multiplicative functions, and integers free of small prime factors.
In the next section we collect some results about applications of arithmetic progressions to m-isometric operators.
for k = 1, 2, 3, are all arithmetic progressions with common difference 2k.
(Readers do, however, need some familiarity with number theory at an undergraduate level and should have taken a first course in modern algebra.) The author begins with a thorough introduction to elementary prime number theory, including Dirichlet's theorem on primes in arithmetic progressions, the Brun sieve, and the Erdos-Selberg proof of the prime number theorem.
Montgomery, Primes in arithmetic progressions, Mich.
Just in case you thought that magic squares were just amusing diversions and had no relevance to any other areas of mathematics, this very problem (construction of a 3 by 3 magic square all of whose entries are squares) has been shown to be highly relevant to problems in various domains, including arithmetic progressions, Pythagorean triangles, and elliptic curves.
We assume without proof the following property of all arithmetic progressions: the sequence [a.sub.1], [a.sub.2], [a.sub.3], ...

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