RIOPLATENSE 1996 Problem 6

Find all integers $k$ for which, there is a function $f: N \to Z$ that satisfies: (i) $f(1995) = 1996$ (ii) $f(xy) = f(x) + f(y) + kf(m_{xy})$ for all natural numbers $x, y$ ,where $m_{xy}$ denotes the greatest common divisor of the numbers $x, y$ .

Clarification: $N = \{1,2,3,...\}$ and $Z = \{...-2,-1,0,1,2,...\}$ .