Counting Additive Decompositions of Quadratic Residues in Finite Fields

Simon R. Blackburn, Sergei V. Konyagin, Igor E. Shparlinski

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 res…