NL-NWO 1999 Problem 1

Let $f: \mathbb{Z} \rightarrow \{-1,1\}$ be a function such that $$f(mn) =f(m)f(n),\ \forall m,n \in \mathbb{Z}.$$ Show that there exists a positive integer $a$ such that $1 \leq a \leq 12$ and $f(a) = f(a + 1) = 1$ .