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arXiv · 2304.13801

Additive decompositions of large multiplicative subgroups in finite fields

Chi Hoi Yip
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Abstract

We show that a large multiplicative subgroup of a finite field $\mathbb{F}_q$ cannot be decomposed into $A+A$ or $A+B+C$ nontrivially. We also find new families of multiplicative subgroups that cannot be decomposed as the sum of two sets nontrivially. In particular, our results extensively generalize the results of S\'{a}rk\"{o}zy and Shkredov on the additive decomposition of the set of quadratic residues modulo a prime.

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Chi Hoi Yip. 2023-04-26. Additive decompositions of large multiplicative subgroups in finite fields. https://doi.org/10.4064/aa230330-21-2

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