Dirichlet's theorem on arithmetic progressions
Teorema de Dirichlet sobre progresiones aritméticas
- Date
- 1837 · confidence high
- Place
- Berlin, Germany
- Credited to
- Johann Peter Gustav Lejeune Dirichlet
- Field
- Knowledge & symbols
What was discovered
A number-theory theorem proving that every arithmetic progression a+nd, with a and d coprime, contains infinitely many primes. It extends Euclid's theorem on the infinitude of primes and was the first use of analysis (L-functions) in number theory.
Proved by Dirichlet in 1837 using L-functions, a pioneering analytic technique in number theory.
What it led to
- the birth of analytic number theory (Dirichlet L-functions)
- later results on the distribution of primes in progressions
- a conceptual extension of Euclid's theorem on infinite primes