An Application of Modular Hyperbolas to Quadratic Residues
Mizan R. Khan and Richard Magner, Richard Magner · American Mathematical Monthly · 2015
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 ≡ 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.