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• ... It seems to be saying Sum{p==a(mod q)}[1/p] = (Sum[divergent to +oo] + Sum[all positive] + Sum[Convergent] ) * (non-zero positive) + O(1) which
Message 1 of 2 , Apr 29, 2002
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--- Jon Perry <perry@...> wrote:
> At:
>
> http://algo.inria.fr/banderier/Seminar/Vardi/index.html
>
> is the immortal statement:
>
> sigma(p eqv. a mod q, 1/p) = infinity
>
> i.e. Dirichlet's Theorem. (the sum of the primes 1/p for
> p=amodq=a+kq is
> infinite).
>
> Apparently, the fact that there are an infinite number of primes in
> a+kq
> implies the sum of these primes is infinite.

It seems to be saying

Sum{p==a(mod q)}[1/p]
= (Sum[divergent to +oo]
+ Sum[all positive]
+ Sum[Convergent] ) * (non-zero positive) + O(1)

which obviously diverges to +oo.

To be honest, your 'apparently' sentence confuses me as to what you
have problems with. The maths on that page in no way says what you
have claimed it says. The only 'funny' logic is yours.

Phil

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