  We study the search problem class $\mathrm{PPA}_q$ defined as a modulo-$q$
analog of the well-known $\textit{polynomial parity argument}$ class
$\mathrm{PPA}$ introduced by Papadimitriou '94. Our first result shows that
this class can be characterized in terms of $\mathrm{PPA}_p$ for prime $p$.
  Our main result is to establish that an $\textit{explicit}$ version of a
search problem associated to the Chevalley--Warning theorem is complete for
$\mathrm{PPA}_p$ for prime $p$. This problem is $\textit{natural}$ in that it
does not explicitly involve circuits as part of the input. It is the first such
complete problem for $\mathrm{PPA}_p$ when $p \ge 3$.
  Finally we discuss connections between Chevalley-Warning theorem and the
well-studied $\textit{short integer solution}$ problem and survey the
structural properties of $\mathrm{PPA}_q$.
