Problem 63:

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 nth power?

```
```package runner;
import java.math.BigInteger;
import java.util.HashSet;
class runner
{
public static void main (String[] args) throws java.lang.Exception
{
long time = System.currentTimeMillis();
HashSet store = new HashSet();
int power=1;
boolean found = true;
while(found){
found = false;
BigInteger base = BigInteger.ONE;
do{
BigInteger r = base.pow(power);
if(r.toString().length() > power) break;
if(r.toString().length() == power){
store.add(r.toString());
found = true;
}
base = base.add(BigInteger.ONE);
}while(true);
power++;
}
System.out.println(store.size());
System.out.println("time:"+(System.currentTimeMillis()-time));
}
}