A friend of mine recently asked me this question.
For a positive integer $n$, a function $f(n)$ is defined as:
$f(n)=$ sum of digits in $n$.
given $f(n)=5$ find the maximum value of $f(n^5)$.
I tried solving this problem by putting random values, but my friend gave me a hint that the answer is greater than 100. Now I am completely lost because I couldn't find a single $n$ for which the value of $f(n^5)$ comes out to be greater than 100. Is there a proper way to solve it?