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arXiv · 0801.2021

Additive properties of product sets in an arbitrary finite field

Alexey Glibichuk
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Abstract

It is proved that for any two subsets $A$ and $B$ of an arbitrary finite field $\Fq$ such that $|A||B|>q$ the identity $16AB=\Fq$ holds. Moreover, it is established that for every subsets $X, Y\subset \Fq$ with the property $|X||Y|\geqslant 2q$ the equality $8XY=\Fq$ holds.

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Alexey Glibichuk. 2008-01-14. Additive properties of product sets in an arbitrary finite field. https://arxiv.org/abs/0801.2021

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