  Presented is the exact solution of the problem of finding a potential of an
inflaton scalar field for which adiabatic perturbations generated during a de
Sitter (inflationary) stage in the early Universe have the exactly flat (or,
the Harrison-Zeldovich) initial spectrum. This solution lies outside the scope
of the slow-roll approximation and higher-order corrections to it. The
potential found depends on two arbitrary physical constants, one of those
determines an amplitude of perturbations. For small (zero) values of the other
constant, a long (infinite) inflationary stage with slow rolling of the
inflaton field exists.
