# Dependent on \(m\)?

**Number Theory**Level 3

For each number \(n\), we define the "Digital Sum" as sum of the digits of \(n\) and repeat the process until the result is a single digit number.

Example :

For \( 1234 \rightarrow 1 + 2 + 3 + 4 \rightarrow 10 \rightarrow 1 + 0 = 1 \)

Find the digital sum of \(\underset { m \text{ times} }{ \underbrace { 4617\ldots 4617} } \).

\( m > 0 \).

Inspired by 2016 Digital Sum