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.
Original language | English |
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Pages (from-to) | 223-227 |
Number of pages | 5 |
Journal | Functiones et Approximatio, Commentarii Mathematici |
Volume | 52 |
Issue number | 2 |
DOIs | |
Publication status | Published - Jun 2015 |
Externally published | Yes |
Keywords
- Additive decompositions
- Finite fields
- Quadratic nonresidues character sums