Definition:Additive Function (Number Theory)

This page is about additive functions in number theory. For other uses, see Definition:Additive Function.

Definition

Let $f: \Z \to \Z$ be a function on the integers $\Z$.

Let $m, n \in \Z$.

Then $f$ is described as additive iff:

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

That is, an additive function is one where the value of a product of two coprime numbers equals the sum of the value of each one individually.

Also see

Compare with Completely Additive Function.