I was interested in the subject of quadratic residues recently. Let be an odd prime. We say that an integer is a quadratic residue iff there exists an integer such that otherwise we say that is a quadratic non-residue

Let be the set of all quadratic residues Then, you know what? is a subgroup of index of the multiplicative group of the field of integers This is not mentioned in a number of books and websites on quadratic residues I've seen, but I think a development based on this group-theoretic approach can advance our understanding of results in number theory, in particular quadratic residues.

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