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Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma
Proving Dirichlet's Theorem On Arithmetic Progressions, Owen T. Abma
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First proved by German mathematician Dirichlet in 1837, this important theorem states that for coprime integers a, m, there are an infinite number of primes p such that p = a (mod m). This is one of many extensions of Euclid’s theorem that there are infinitely many prime numbers. In this paper, we will formulate a rather elegant proof of Dirichlet’s theorem using ideas from complex analysis and group theory.