Let $f: Z^+ \to Z^+ \cup \{0\}$ a function that meets the following conditions: a) $f (a b) = f (a) + f (b)$, b) $f (a) = 0$ provided that the digits of the unit of $a$ are $7$, c) $f (10) = 0$. Find $f (2016).$
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist F3 day2 (F= Functions)
Tags: Digits, functional equation, functional, algebra