On the reducibility of large sets of residues modulo p

Gyarmati, Katalin and Konyagin, Sergei and Sárközy, András (2013) On the reducibility of large sets of residues modulo p. Journal of Number Theory, 133 (7). pp. 2374-2397. ISSN 0022-314X

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Abstract

It is shown that if p>2 and C is a subset of $F_p$ with $|C| \ge p-C_1\frac{p}{\log p}$ then there are $A\in F_p$, $B\in F_p$ with $C=A+B$, $A\ge 2$, $B\ge 2$. On the other hand, for every prime p there is a subset $C\subset F_p$ with $ |C|> p-C_2\frac{\log\log p}{(\log p)^{1/2}}$ such that there are no $A, B$ with these properties.

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