Problem 63

Powerful digit counts

The 5-digit number, 16807=7⁵, is also a fifth power. Similarly, the 9-digit number, 134217728=8⁹, is a ninth power.

五位数16807同时是7的五次方，同样地，九位数134217728是8的九次方。

How many n-digit positive integers exist which are also an nth power?

有多少个n位数正整数，这些正整数同时是某个数字的n次方？

from power import power

count = 0

for i in range(1, 100):

    for p in range(1, 100):

        num = power(i, p)

        if len(str(num)) == p:

            print(i, p, num)

            count += 1

print(count)

# power.py

def power(x, y):

    if y == 1:

        return x

    tot = 1

    for i in range(y):

        tot *= x

    return tot

if __name__ == '__main__':

    for x in range(1, 5):

        for y in range(1, 5):

            print('power({0}, {1}) = {2}'.format(x, y, power(x, y)))

巴特西

Problem 63

Problem 63

Powerful digit counts

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