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The square of the sum of the digits of k function

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November 9, 2010
functionlogarithmsmodular arithmeticalgebra unsolvedalgebra

Problem Statement

For a positive integer kk, let f1(k)f_1(k) be the square of the sum of the digits of kk. Define fn+1f_{n+1} = f1∘fnf_1 \circ f_n . Evaluate f2007(22006)f_{2007}(2^{2006} ).
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