Show that: a) There is a sequence of non-zero natural numbers $a_1, a_2, ...$ uniquely determined, so that: $n = \sum _ {d | n} a _ d$ for whatever $n \in N ^ {*}$ . b) There is a sequence of non-zero natural numbers $b_1, b_2, ...$ uniquely determined, so that: $n = \prod _ {d | n} b _ d$ for whatever $n \in N ^ {*}$ . Note: The sum from a), respectively the product from b), are made after all the natural divisors $d$ of the number $n$ , including $1$ and $n$ .