# Definition:Multiplicative Arithmetic Function

## Definition

Let $f : \N \to \C$ be an arithmetic function.

Then $f$ is multiplicative if and only if:

$m \perp n \implies f \left({m n}\right) = f \left({m}\right) f \left({n}\right)$

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.

## Also see

• Results about multiplicative functions can be found here.