  A strict bidimensional (strict-2D) exact-exchange (EE) formalism within the
framework of density-functional theory (DFT) has been developed and applied to
the case of an electron gas subjected to a strong perpendicular magnetic field,
that drives the system to the regime of the integer quantum Hall effect (IQHE).
As the filling of the emerging Landau levels proceeds, two main features
results: i) the EE energy minimizes with a discontinuous derivative at every
integer filling factor $\nu$; and ii) the EE potential display sharp
discontinuities at every integer $\nu$. The present contribution provides a
natural improvement as compared with the widely used local-spin-density
approximation (LSDA), since the EE energy functional fully contains the effect
of the magnetic field, and includes an inter-layer exchange coupling for
multilayer systems. As a consistency test, the LSDA is derived as the leading
term of a low-field expansion of the EE energy and potential.
