13th British Mathematical Olympiad 1977 Problems

13th British Mathematical Olympiad 1977 Problems1.  f(n) is a function on the positive integers with non-negative integer values such that: (1) f(mn) = f(m) + f(n) for all m, n; (2) f(n) = 0 if the last digit of n is 3; (3) f(10) = 0. Show that f(n) = 0 for all n.