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Topic: Early (1930's) work on arithmetic progressions
Replies: 10   Last Post: Oct 1, 2017 11:40 AM

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William Elliot

Posts: 2,626
Registered: 1/8/12
Re: Early (1930's) work on arithmetic progressions
Posted: Sep 27, 2017 11:14 PM
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> On Wednesday, September 27, 2017 at 8:09:45 PM UTC+1, Paul wrote:

> > https://dml.cz/…/1033…/122006/CasPestMatFys_067-1938-4_3.pdf
> > I'm trying to understand some of the early work on arithmetic
> > progressions. In the above paper, I don't understand how van der
> > Waerden's theorem is used to prove (8) on page 236. It's true that
> > one of the sets in the partition will contain arithmetic
> > progressions of length k. But, in the partition of the integers
> > from 1 to r_k * n_0, an A_i will have lots of members which are
> > not in the a_i maximal sequence. So I don't see how an A_i with an
> > arithmetical progression of length k establishes a contradiction.

>
> I just noticed that the URL doesn't display in a very user-friendly
> way (at least in my newsreader).
> /dml.cz/bitstream/handle/10338.dmlcz/122006/CasPestMatFys_067-1938-4_3.pdf
> is the URL without the https:// preface. I hope that comes out
> better.


The first one is a diaster. The second written as
http://dml.cz/bitstream/handle/10338.dmlcz/122006/CasPestMatFys_067-1938-4_3.pdf

should be openable by all. PDF, not being particularily friendly, is
a deterent to considering your question.



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