Category:Dirichlet's Theorem on Arithmetic Sequences

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This category contains pages concerning Dirichlet's Theorem on Arithmetic Sequences:


Let $a, q$ be coprime integers.

Let $\PP_{a, q}$ be the set of primes $p$ such that $p \equiv a \pmod q$.


Then $\PP_{a, q}$ has Dirichlet density:

$\map \phi q^{-1}$

where $\phi$ is Euler's phi function.


In particular, $\PP_{a, q}$ is infinite.


Source of Name

This entry was named for Johann Peter Gustav Lejeune Dirichlet.