Question 80206
<pre><font size = 5><b>
A function f(n) defined for all positive integers
has the property that f(m) + f(n) = f(mn) for any 
two positive integers m and n.  if f(2)= 7 and 
f(3)=10, then calculate f(12).

f(12) = f(4·3) = f(4) + f(3) = f(4) + 10 = 

f(2·2) + 10 = [f(2) + f(2)] + 10 = [7 + 7] + 10 =

14 + 10 = 24.

-------------------------------

Another way:

f(12) = f(2·6) = f(2) + f(6) = 7 + f(6) = 7 + f(2·3) =

7 + [f(2) + f(3)] = 7 + [7 + 10] = 7 + 17 = 24. 

Edwin</pre>