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2019 A note on the set $A(A+A)$
Pierre-Yves Bienvenu, François Hennecart, Ilya Shkredov
Mosc. J. Comb. Number Theory 8(2): 179-188 (2019). DOI: 10.2140/moscow.2019.8.179

Abstract

Let p be a large enough prime number. When A is a subset of Fp\{0} of cardinality |A|>(p+1)3, then an application of the Cauchy–Davenport theorem gives Fp\{0}A(A+A). In this note, we improve on this and we show that |A|0.3051p implies A(A+A)Fp\{0}. In the opposite direction we show that there exists a set A such that |A|>(18+o(1))p and Fp\{0}A(A+A).

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Pierre-Yves Bienvenu. François Hennecart. Ilya Shkredov. "A note on the set $A(A+A)$." Mosc. J. Comb. Number Theory 8 (2) 179 - 188, 2019. https://doi.org/10.2140/moscow.2019.8.179

Information

Received: 21 November 2018; Revised: 14 December 2018; Accepted: 29 March 2019; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07063274
MathSciNet: MR3959885
Digital Object Identifier: 10.2140/moscow.2019.8.179

Subjects:
Primary: 11B75

Rights: Copyright © 2019 Mathematical Sciences Publishers

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