can you offer a proof for this proposition?
$$\frac{1}{d}\sum_{o(\chi )|d} {\chi (u) = \left\{ {\begin{array}{*{20}{c}} {1 \quad \text{if u is a dth power resedue modulo p}}\\ {0 \quad \text{otherwise}} \end{array}} \right.}$$
$o(\chi)=d$ means order of $\chi$ modulo $p$ is $d$.