For a given positive integer denote the square of the sum of its digits by and let Determine the value of
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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
Školjka 
denote the square of the sum of its digits by 
and let 
Determine the value of 