Counting additive decompositions of quadratic residues in finite fields

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

Research output: Contribution to journalArticle

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)223-227
Number of pages5
JournalFunctiones et Approximatio, Commentarii Mathematici
Issue number2
Publication statusPublished - Jun 2015
Externally publishedYes


  • Additive decompositions
  • Finite fields
  • Quadratic nonresidues character sums

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