The aim of the present article is to derive an exact integral equation for the Green function of the
Hubbard model through an equation-of-motion procedure, like in the original Hubbard papers. Though
our exact integral equation does not allow to solve the Hubbard model, it represents a strong
constraint on its approximate solutions. An analogous sum rule has been already obtained in the
literature, through the use of a spectral moment technique. We think however that our
equation-of-motion procedure can be more easily related to the historical procedure of the original
Hubbard papers. We also discuss examples of possible applications of the sum rule and propose and
analyse a solution, fulfilling it, that can be used for a pedagogical introduction to the
Mott–Hubbard metal-insulator transition.