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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
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