Gaeta G., Rodriguez M.A. On discrete symmetries of differential equations (29K, TeX) ABSTRACT. We propose a method to determine a special class of discrete symmetries - which we call quantized - of differential equations, based on solution of a linear functional equation. By the same method, we can determine differential equations possessing a given quantized symmetry by solving a linear (standard, i.e. non functional) PDE. Geometrical motivation and interpretation are also given, together with simple but physically significant examples.