RIOPLATENSE 1993 Problem 1

Find all functions $f$ defined on the integers greater than or equal to $1$ that satisfy: (a) for all $n,f(n)$ is a positive integer. (b) $f(n + m) =f(n)f(m)$ for all $m$ and $n$ . (c) There exists $n_0$ such that $f(f(n_0)) = [f(n_0)]^2$ .