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arXiv · 1403.2589

Counting Additive Decompositions of Quadratic Residues in Finite Fields

Simon R. Blackburn·Sergei V. Konyagin·Igor E. Shparlinski
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Abstract

We say that a set $S$ is additively decomposed into two sets $A$ and $B$ if $S = \{a+b : a\in A, \ b \in B\}$. A. Sárközy has recently conjectured that the set $Q$ of quadratic residues modulo a prime $p$ does not have nontrivial decompositions. Although various partial results towards this conjecture have been obtained, it is still open. Here we obtain a nontrivial upper bound on the number of such decompositions.

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Simon R. Blackburn, Sergei V. Konyagin, Igor E. Shparlinski. 2014-03-11. Counting Additive Decompositions of Quadratic Residues in Finite Fields. https://arxiv.org/abs/1403.2589

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