IMO Shortlist 1990 problem 8
Dodao/la:
arhiva2. travnja 2012. For a given positive integer
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
denote the square of the sum of its digits by
![f_1(k)](/media/m/9/9/3/993c7fd6e208576fbcb6ecf55aeb52ba.png)
and let
![f_{n+1}(k) = f_1(f_n(k)).](/media/m/8/1/7/817450a57c3821a0f102ce81bc4176d1.png)
Determine the value of
%V0
For a given positive integer $k$ denote the square of the sum of its digits by $f_1(k)$ and let $f_{n+1}(k) = f_1(f_n(k)).$ Determine the value of $f_{1991}(2^{1990}).$
Izvor: Međunarodna matematička olimpijada, shortlist 1990