I know that given m, n with gcd(m,n)=1 you can split k into two relatively prime factors in a suitable way depending on m and n.
Anyway, help is appreciated!
How do you know that the domain is the set of integers?
If f is multiplicative, then for all k,n. Then , which is also multiplicative. Also we know that so we don't have to worry about dividing by zero or anything like that...