Question 47
Let $k \geq 1$ be a natural number. Determine as a function of $k$ the number of positive integers $n$ with the following properties:
a. in base ten is written with $k$ digits, all odd;
b. are divisible by $5$, and the quotient $\frac{n}{5}$, written in base ten, still has $k$ digits, all odd.
a. in base ten is written with $k$ digits, all odd;
b. are divisible by $5$, and the quotient $\frac{n}{5}$, written in base ten, still has $k$ digits, all odd.