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ARITHMETIC AND GEOMETRIC PROGRESSIONS IN PRODUCT SETS OVER FINITE FIELDS
Published online by Cambridge University Press: 01 December 2008
Abstract
Given two sets of elements of the finite field 𝔽q of q elements, we show that the product set contains an arithmetic progression of length k≥3 provided that k<p, where p is the characteristic of 𝔽q, and #𝒜#ℬ≥3q2d−2/k. We also consider geometric progressions in a shifted product set 𝒜ℬ+h, for f∈𝔽q, and obtain a similar result.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 78 , Issue 3 , December 2008 , pp. 357 - 364
- Copyright
- Copyright © 2009 Australian Mathematical Society