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Note on an additive characterization of quadratic residues modulo $$p$$. (English) Zbl 1231.11005
Summary: It is shown that an even partition $$A\cup B$$ of the set $$\mathcal R = \{1, 2, \dots, p-1\}$$ of positive residues modulo an odd prime $$p$$ is the partition into quadratic residues and quadratic nonresidues if and only if the elements of $$A$$ and $$B$$ satisfy certain additive properties, thus providing a purely additive characterization of the set of quadratic residues.

##### MSC:
 11A15 Power residues, reciprocity 11T24 Other character sums and Gauss sums