The Dirichlet Convolution is this:
The arithmetic function is said to be the inverse of the arithmetic function if . Show
that the arithmetic function has an inverse if and only if . Show that if has an inverse it is
unique. (Hint: When , find the inverse of by calculating recursively, using the
fact that .)
I'm really stumped on how to approach this one. Obviously the inverse doesn't exist when , but beyond that, how do I tackle this one?