Question 120
the sum of the digits of a number - let us denote by $s(n)$ the sum of the numbers in the number $n$. For example $s(2345)=2+3+4+5=14$. Let us note that:
$40-s(40)=36=9 \times 4 ; 500-s(500)=495=9 \times 55 ; 2345-s(2345)=2331=9 \times 259$.
a. What can we say about the number $n-s(n)$ ?
b. Using the previous item calculate $s\left(s\left(s\left(2^{2009}\right)\right)\right.$ ). Suggestion: Show that the number sought is less than 9.
$40-s(40)=36=9 \times 4 ; 500-s(500)=495=9 \times 55 ; 2345-s(2345)=2331=9 \times 259$.
a. What can we say about the number $n-s(n)$ ?
b. Using the previous item calculate $s\left(s\left(s\left(2^{2009}\right)\right)\right.$ ). Suggestion: Show that the number sought is less than 9.