lean_workbook_plus_55691

We note that $f(ka) = kf(a)$ for all positive integers $k$ by writing $f(ka) = f(a + a + a + .... + a) = f(a) + f(a + a + .. + a) = f(a) + f(a) + f(a + a + ... + a) = ...$ , where each step removes one $a$ from inside the function and adds an $f(a)$ outside the bracket. \n\nThus, $f(2008) = 2008\cdot f(1)$ , and $f(2009) = 2009 \cdot f(1)$ . \n\nTherefore, $f(1) = \frac{f(2008)}{2008} = \frac{f(2009)}{2009}$ . Plug-n-chug from there.