\begin{definition}[Definition:Multiplicative Arithmetic Function]
Let $f : \N \to \C$ be an arithmetic function.
Then $f$ is '''multiplicative''' {{iff}}:
:$m \perp n \implies \map f {m n} = \map f m \map f n$
where $m \perp n$ denotes that $m$ is coprime to $n$.
That is, a '''multiplicative function''' is one where the value of a product of two coprime numbers equals the product of the value of each one individually.
\end{definition}