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ARITHMETIC AND GEOMETRIC PROGRESSIONS IN PRODUCT SETS OVER FINITE FIELDS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 78 / Issue 3 / December 2008
- Published online by Cambridge University Press:
- 01 December 2008, pp. 357-364
- Print publication:
- December 2008
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- Article
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- You have access
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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.
of elements of the finite field 𝔽
