  Let $r$ and $k$ be positive integers with $r \mid k$. Denote by
$w_{\mathrm{\mathfrak{z}}}(k;r)$ the minimum integer such that every coloring
$\chi:[1,w_{\mathrm{\mathfrak{z}}}(k;r)] \rightarrow \{0,1,\dots,r-1\}$ admits
a $k$-term arithmetic progression $a,a+d,\dots,a+(k-1)d$ with $\sum_{j=0}^{k-1}
\chi(a+jd) \equiv 0 \,(\mathrm{mod }\,r)$. We investigate these numbers as well
as a "mixed" monochromatic/zero-sum analogue. We also present an interesting
reciprocity between the van der Waerden numbers and
$w_{\mathrm{\mathfrak{z}}}(k;r)$.
