LaTeX Error: There's no line here to end - wie kann ich die Zeile trotzdem umbrechen?

Was Du da vorhast geht so nicht und ist auch ganz schlechter Stil. Diese Art des Zeilenumbruchs sollte vermieden werden.

Es gibt mit »amsthm« und »ntheorem« zwei ähnliche Pakete und damit zwei Möglichkeiten. Beide Lösungen werden hier dargestellt.

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\documentclass[ngerman]{scrartcl}
\usepackage[T1]{fontenc}
\usepackage{selinput}
\SelectInputMappings{
  adieresis={ä},
  germandbls={ß}
}
\usepackage{babel}
\usepackage{mathtools}  % lädt »amsmath«
\usepackage{amsthm}
\newtheoremstyle{linebreak}   % name
{3pt}                         % Space above
{3pt}                         % Space below
{}                            % Body font
{}                            % Indent amount 1
{\bfseries}                   % Theorem head font
{\newline}                    % Punctuation after theorem head
{.5em}                        % Space after theorem head 2
{}                            % Theorem head spec (can be left empty, meaning ‘normal’)
\theoremstyle{linebreak}
\newtheorem{satz}{Satz}
\begin{document}
  \begin{satz}[Satz von Euler-Fermat]
    Wenn $\mathrm{ggT}(a,n) = 1$, dann gilt
    \[
      a^{\varphi(n)} \equiv 1\,(\mathrm{mod}\,n)
    \]
  \end{satz}
\end{document}
 
 
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\documentclass[ngerman]{scrartcl}
\usepackage[T1]{fontenc}
\usepackage{selinput}
\SelectInputMappings{
  adieresis={ä},
  germandbls={ß}
}
\usepackage{babel}
\usepackage{mathtools}  % lädt »amsmath«
\usepackage[amsmath]{ntheorem}
\theoremstyle{break}
\newtheorem{satz}{Satz}
\begin{document}
  \begin{satz}[Satz von Euler-Fermat]
    Wenn $\mathrm{ggT}(a,n) = 1$, dann gilt
    \[
      a^{\varphi(n)} \equiv 1\,(\mathrm{mod}\,n)
    \]
  \end{satz}
\end{document}
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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Aussuchen musst Du aber selbst. Du kannst natürlich noch weitere Formatierungen vornehmen. Ein Blick in die Anleitung des jeweiligen Pakets ist dabei ein guter Start.