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\documentclass[11pt,parskip=half,headsepline,headinclude,headlines=3.25,DIV=14]{scrartcl}

\usepackage[T1]{fontenc}
\usepackage[latin1]{inputenc}
\usepackage[ngerman]{babel}


\begin{document}

\paragraph{Aufgabe 1.}

\newpage

\setcounter{page}{1}

\paragraph{Aufgabe 2.}

\newpage

\setcounter{page}{1}

\paragraph{Aufgabe 3.}

\newpage

\setcounter{page}{1}

\paragraph{Aufgabe 4.}
\end{document}

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\g@addto@macro\size@paragraph{\setcounter{page}{1}}