ABSTRACT
In 1840, Dirichlet proved his famous theorem on the infinitude of primes in arithmetic progressions. This states that given integers 1 ≤ a, q ∈ ℤ with https://www.w3.org/1998/Math/MathML"> ( a , q ) = 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138747022/abb99e87-ffb7-4196-a4c4-acb0033e3d6a/content/eq435.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> , there are infinitely many primes p with https://www.w3.org/1998/Math/MathML"> p ≡ a ( mod q ) . https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138747022/abb99e87-ffb7-4196-a4c4-acb0033e3d6a/content/eq436.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
