Question 72
For any positive integer $n$, define $a_n = \{\frac{n}{s(n)}\}$, where $s(k)$ represents the sum of the digits of the natural number $k$, and $\{x\}$ is the fractional part of the real number $x$.
a) Prove that there exist infinitely many positive integers $n$ such that $a_n = \frac{1}{2}$.
b) Determine the smallest positive integer $n$ such that $a_n = \frac{1}{6}$.
a) Prove that there exist infinitely many positive integers $n$ such that $a_n = \frac{1}{2}$.
b) Determine the smallest positive integer $n$ such that $a_n = \frac{1}{6}$.