Re: Goldbach's Conjecture

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#1248

From: Felipe Voloch
Date: Thu, 10 Sep 1998 00:00

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Paul Bruckman (aardwolf@gte.net) wrote:
: It seems to me that the natural tool that might be used to prove
: Goldbach's Conjecture is the square of the series of x^p, where the
: powers are the odd primes.  This produces a series of terms A(n)* x^2n,
: going from n=3 to inf. , and GC would then be equivalent to proving that
: A(n) > 0 for all such n.  Of course, A(n) is odd iff n is prime,
: corresponding to the representation 2n = n+n, which can only occur in
: one way, whereas all other representations of 2n occur in pairs.  
: 
: Has anyone thought about this approach, and if so, does anyone see any
: kind of revelation that might prove A(n)>0 for all n?  Paul Bruckman
: 


This is the first step in the Hardy-Littlewood method. The next step
is to write A(n) as an integral, using Cauchy's formula. Then the fun
starts...

Felipe

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From: voloch@fireant.ma.utexas.edu (Felipe Voloch)
Subject: Re: Goldbach's Conjecture
Date: 1998/09/10
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