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Twins ofk-free numbers in arithmetic progressions

✍ Scribed by Zaizhao Meng

Publisher
Akadmiai Kiad
Year
2010
Tongue
English
Weight
700 KB
Volume
130
Category
Article
ISSN
1588-2632

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πŸ“œ SIMILAR VOLUMES

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Given a sequence B of relatively prime positive integers with the sum of inverses finite, we investigate the problem of finding B-free numbers in short arithmetic progressions.

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We show that if G is a K r -free graph on N, there is an independent set in G which contains an arbitrarily long arithmetic progression together with its difference. This is a common generalization of theorems of Schur, van der Waerden, and Ramsey. We also discuss various related questions regarding

ORDINAL NUMBERS IN ARITHMETIC PROGRESSIO
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## Abstract The class of all ordinal numbers can be partitioned into two subclasses in such a way that neither subclass contains an arithmetic progression of order type Ο‰, where an arithmetic progression of order type Ο„ means an increasing sequence of ordinal numbers (ß + δγ)Ξ³<Ξ³<>r, Ξ΄ β‰  0.