8

Part of 1990 IMO Shortlist

Problems(1)

Square of the sum of its digits

Source: IMO ShortList 1990, Problem 8 (HUN 1)

For a given positive integer

k

denote the square of the sum of its digits by

f_1(k)

and let f_{n\plus{}1}(k) \equal{} f_1(f_n(k)). Determine the value of

f_{1991}(2^{1990}).

number theoryDigitssum of digitsCalculatedecimal representationIMO Shortlist