Given an Arithmetic Series of terms , for , 2, ..., the series contains an infinite number of Primes
if and are Relatively Prime, i.e., . Dirichlet proved this theorem using Dirichlet *L*-Series.

**References**

Courant, R. and Robbins, H. ``Primes in Arithmetical Progressions.'' §1.2b in Supplement to Ch. 1 in
*What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.*
Oxford, England: Oxford University Press, pp. 26-27, 1996.

Shanks, D. *Solved and Unsolved Problems in Number Theory, 4th ed.* New York: Chelsea, pp. 22-23, 1993.

© 1996-9

1999-05-24