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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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Paul

Posts: 773
Registered: 7/12/10
Early (1930's) work on arithmetic progressions
Posted: Sep 27, 2017 3:09 PM
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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.

Many thanks for your help.

Paul Epstein



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