## Project Euler Problem 63 Solution

## Question

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?

## Haskell

```
main :: IO ()
main = print $ sum $ [1 | i <- [1..99], n <- [1..99], length (show (i^n)) == n]
```

```
$ ghc -O2 -o nPower nPower.hs
$ time ./nPower
real 0m0.026s
user 0m0.024s
sys 0m0.000s
```

## Python

```
#!/usr/bin/env python
print(sum(1 for i in range(1,100) for x in range(1,100) if len(str(i**x)) == x))
```

```
$ time python3 n-power.py
real 0m0.030s
user 0m0.020s
sys 0m0.008s
```

Questions? Comments? Send me an email: z@chdenton.com