BG-MO 1993 Problem 1

Find all functions $f$ , defined and having values in the set of integer numbers, for which the following conditions are satisfied: (a) $f(1) = 1$ ; (b) for every two whole (integer) numbers $m$ and $n$ , the following equality is satisfied: $$f(m+n)·(f(m)-f(n)) = f(m-n)·(f(m)+ f(n))$$