# 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?

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   0m0.022s
user   0m0.020s
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   0m0.021s
user   0m0.020s
sys    0m0.000s