From: Alexander Bogomolny Subject: Re: Number Theory question Date: Tue, 19 Dec 2000 22:02:33 EST Newsgroups: sci.math Summary: [missing] lena wrote: > > Show that there are infinitely many primes of the type 4n+3, and of the type > 6n+5. > > This is an easy consequence of Dirchlet's theorem that says that are > infinitely many primes of the type an + b, with a and b relatively prime. > > However, the obove question should be a lot easier to prove without using > such a powerful theorem. I can't see a proof yet. Theorem 98 (p 173) from "Introduction to Number Theory" by T. Nagell (Chelsea Publishing, 1981, distributed by AMS) states "If n is a natural number, there are infinitely many primes which are = -1 (mod n)." The proof does not use Dirichlet's theorem but takes 4 Lemmas over the space of 3 pages. Alexander Bogomolny, http://www.cut-the-knot.com