PlanetMath: Dirichlet's theorem on primes in arithmetic progressions

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Dirichlet's theorem on primes in arithmetic progressions

(Theorem)

If $a$ is a positive integer and $(a,b)=1$ with $b$ an integer, then there are infinitely many primes of the form $an + b$ with $n$ an integer.

"Dirichlet's theorem on primes in arithmetic progressions" is owned by vitriol.

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Keywords:

Dirichlet Prime

Attachments:: special case of Dirichlet's theorem on primes in arithmetic progressions (Theorem) by bbukh
there are an infinite number of primes $\equiv \pm 1\pmod 4$ (Theorem) by rm50
there are an infinite number of primes $\equiv 1\mod m$ (Theorem) by rm50
table of primes in arithmetic progressions per Dirichlet's theorem (Data Structure) by PrimeFan

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Cross-references: primes, integer, positive
There are 7 references to this entry.

This is version 6 of Dirichlet's theorem on primes in arithmetic progressions, born on 2002-02-16, modified 2002-05-07.
Object id is 2000, canonical name is DirichletsTheorem.
Accessed 8733 times total.

Classification:

11N13 (Number theory :: Multiplicative number theory :: Primes in progressions)

Pending Errata and Addenda

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