Definition:Additive Arithmetic Function

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

Definition

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


Then $f$ is additive if and only if:

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


Also see