An Application of Modular Hyperbolas to Quadratic Residues.
AMERICAN MATHEMATICAL MONTHLY(2015)
Abstract
There are many elementary proofs of the classical result that -1 is a quadratic residue of an odd prime p if and only if p equivalent to 1 (mod 4). In this note we prove this result by using the symmetries of a modular hyperbola. Consequently, our proof has a more geometric flavor than many of the other proofs.
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