We study positive solutions of the following polyharmonic equation with Hardy weights associated to Navier boundary conditions on a half space: (0.1) $$\left\{ {\begin{array}{*{20}c} {( - \Delta )^m u(x) = \frac{{u^p (x)}} {{\left| x \right|^s }},} & {in \mathbb{R}_ + ^n ,} \\ {u(x) = - (\Delta )u(x) = \cdots = ( - \Delta )^{m - 1} u(x) = 0,} & {on \partial \mathbb{R}_ + ^n ,} \\ \end{array} } \right.$$ where m is any positive integer satisfying 0 < 2m < n. We first prove that the positive solutions of (0.1) are super polyharmonic, i.e., (0.2) $${\left( { - \Delta } \right)^i}u > 0,\;i = 0,1, \ldots ,m - 1.$$ For α = 2m, applying this important property, we establish the equivalence between (0.1) and the integral (0.3) $$u \left( x \right) = {c_n}\int_{\mathbb{R}_ + ^n} {\left( {\frac{1}{{{{\left| {x - y} \right|}^{n - \alpha }}}} - \frac{1}{{{{\left| {{x^*} - y} \right|}^{n - \alpha }}}}} \right)} \frac{{{u ^p}\left( y \right)}}{{{{\left| y \right|}^s}}}dy,$$ where x* = (x 1,..., x n−1, −x n ) is the reflection of the point x about the plane R n−1. Then, we use the method of moving planes in integral forms to derive rotational symmetry and monotonicity for the positive solution of (0.3), in which α can be any real number between 0 and n. By some Pohozaev type identities in integral forms, we prove a Liouville type theorem—the non-existence of positive solutions for (0.1).