Powerful Digit Counts
The $5$-digit number, $16807=7^5$, is also a fifth power. Similarly, the $9$-digit number, $134217728=8^9$, is a ninth power.
How many $n$-digit positive integers exist which are also an $n$th power?
The $5$-digit number, $16807=7^5$, is also a fifth power. Similarly, the $9$-digit number, $134217728=8^9$, is a ninth power.
How many $n$-digit positive integers exist which are also an $n$th power?