Counting Additive Decompositions of Quadratic Residues in Finite Fields

2014/03/11 by Blackburn, Simon R., Konyagin, Sergei V., Shparlinski, Igor E.
#Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1403.2589

Abstract

We say that a set S is additively decomposed into two sets A and B if S = \a+b : a∈ A, b ∈ 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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