- Not to be confused with additive functions, a term with a different meaning used in algebra.
In number theory, additive arithmetic functions are arithmetic functions such that
where means is coprime to . Obviously, must be 0. An example is , the number of distinct prime factors of .
Erdős proved that if a function is additive and increasing then there is some such that for  In particular, if the function is integer-valued then it is uniformly zero.