Since you're using the amsthm package, you could simply redefine the package's \@endtheorem macro to include the \qed instruction, which will place an empty square box at the far right end of the theorem's last line. It's necessary to surround such a redefinition with a pair of \makeatletter and \makeatother instructions because the @ symbol is (deliberately) special in LaTeX. The following MWE shows how this may be achieved.
\documentclass{article}
\usepackage{amsthm}
% redefine the \@endtheorem macro
\makeatletter
\def\@endtheorem{\qed\endtrivlist\@endpefalse } % insert `\qed` macro
\makeatother
\newtheoremstyle{mythmstyle}{}{}{}{}{\scshape}{.}{ }{}
\theoremstyle{mythmstyle}
\newtheorem{mythm}{Theorem}
\begin{document}
\begin{mythm}[Pythagoras]
Consider a right triangle with sides of length $a$, $b$, and
$c$, and assume w.l.o.g.\ that $a\le b<c$. Then $a^2+b^2=c^2$.
\end{mythm}
\end{document}

Note that this approach, though simple, isn't quite perfect because the qed symbol won't be placed correctly if the theorem ends with a displayed equation. In such cases, you should probably follow the approach provided in Gonzalo's answer, which employs the powerful thmtools package.