##### Wiktionary

**additive function**

n. (context mathematics English) A unary function that preserves the addition operation; a unary function ''f'' such that for any ''x'' and ''y'': ''f''(''x'' + ''y'') = ''f''(''x'') + ''f''(''y'').

##### Wikipedia

**Additive function**

In number theory, an **additive function** is an arithmetic function *f*(*n*) of the positive integer *n* such that whenever *a* and *b* are coprime, the function of the product is the sum of the functions:

*f*(

*ab*) =

*f*(

*a*) +

*f*(

*b*).