Let S(n) be the sum of the digits of the positive integer $n$. Determine $$S(S(S(2003^{2003}))).$$
Source: 2003 Cuba MO 2.7
Tags: number theory, sum of digits
Let S(n) be the sum of the digits of the positive integer $n$. Determine $$S(S(S(2003^{2003}))).$$