Arithmetic Progression


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Related to Arithmetic Progression: geometric progression, harmonic progression

Arithmetic Progression

A sequence of numbers in which the difference between any two succeeding numbers in the sequence is always the same. For example, given the sequence 0, 10, 20, 30, 40, and 50, the progression is arithmetic because the difference between each succeeding number is always 10.
References in periodicals archive ?
Mathematicians have conjectured (but not yet proved) that in the infinite universe of whole numbers, there is no limit to the number of consecutive primes in arithmetic progression.
Thus the arithmetic progression T(k) + 1 + kT(k)t has initial term coprime to its increment and by Dirichlet's Theorem contains infinitely many primes.
Among the topics examined are the distribution of primes (long arithmetic progressions of primes and small gaps between primes), class groups of binary quadratic forms, various aspects of the theory of L-functions, the theory of modular forms, and the study of rational and integral solutions to polynomial equations in several variables.
For centuries, mathematicians have wondered how many arithmetic progressions such as these exist among the set of prime numbers and how long the progressions can get.