2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74920The Law of Quadratic Reciprocity was conjectured by Euler and Legendre who both found an incomplete proof. Gauss called this law "Theorema Fundamentale", and he was the first who gave a complete proof, he also highlighted the equivalence of his formulation with those of Euler and Legrendre. Hereby notes gives a overview of the Theory of Quadratic Residues using a classical approach with some application to Diophantine Equations, such as Two Square Theorem and Pythagorean Quadruplets.52 pagesHistory and Overview11A15 (Primary) 11D09, 11D41 (Secondary)text