From: Robin Chapman <rjc@maths.ex.ac.uk>
Subject: Re: Dirichlet's Theorem
Date: Wed, 12 Jul 2000 18:06:44 GMT
Newsgroups: sci.math
Summary: [missing]

In article <HvukXGAig6a5Ewvc@jboden.demon.co.uk>,
  Jeremy Boden <jeremy@jboden.demon.co.uk> wrote:
>
> But just why is Dirichelet's theorem so difficult to prove?
> Particular choices of A, B are reasonably easy - once you know what
> "trick" to employ...

In Esmonde and Murty's recent book "Problems in Algebraic Number
Theory" they state that there is an elementary proof (of a
precisely defined kind) in the given case a + nx iff
a^2 = 1 (mod n). They don't give a proof, but cite a paper
of Murty.

--
Robin Chapman, http://www.maths.ex.ac.uk/~rjc/rjc.html
 "`The twenty-first century didn't begin until a minute
  past midnight January first 2001.'"
   John Brunner, _Stand on Zanzibar_ (1968)


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