Dirichlet’s Theorem on Primes in Arithmetic Sequences Math 129 Final Paper
نویسنده
چکیده
Dirichlet’s theorem on primes in arithmetic sequences states that in any arithmetic progression m,m + k, m + 2k, m + 3k, . . ., there are infinitely many primes, provided that (m, k) = 1. Euler first conjectured a result of this form, claiming that every arithmetic progression beginning with 1 contained an infinitude of primes. The theorem as stated was conjectured by Gauss, and proved by Dirichlet in 1835. The proof given below follows the original proof rather closely. I believe an elementary proof was found, though it is fairly unenlightening and unintuitive.
منابع مشابه
Dirichlet’s Theorem on Arithmetic Progressions∗
In this paper, we derive a proof of Dirichlet’s theorem on primes in arithmetic progressions. We try to motivate each step in the proof in a natural way, so that readers can have a sense of how mathematics works.
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تاریخ انتشار 2005