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\title{Fun With Functions}
\author{Tobias Nipkow}
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\begin{abstract}
This is a collection of cute puzzles of the form ``Show that if a function
satisfies the following constraints, it must be \dots''
Please add further examples to this collection!
\end{abstract}

Apart from the one about factorial, they all come from the delightful booklet
by Terence Tao~\cite{Tao2006} but go back to Math Olympiads and similar
events.

Please add further examples of this kind, either directly or by sending them
to me. Let us make this a growing body of \emph{fun}!

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