  In a multidimensional infinite layer bounded by two hyperplanes, the Poisson
equation with the polynomial right-hand side is considered. It is shown that
the Dirichlet boundary value problem and the mixed Dirichlet-Neumann boundary
value problem with polynomial boundary conditions have a unique solution in the
class of functions of polynomial growth and it solution is a polynomial. An
algorithm for constructing this polynomial solution is given and examples are
considered.
